The theory of Lie superalgebras. An introduction
From MaRDI portal
Publication:1257956
zbMath0407.17001MaRDI QIDQ1257956
Publication date: 1979
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
Superalgebras (17A70) Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02)
Related Items
Characters of typical irreducible finite-dimensional \({\mathfrak q}(n)\)- modules, Free Lie superalgebras, Complete sets of representations of classical Lie superalgebras, The representations of wreath products via double centralizing theorems, Quantized enveloping algebras associated with simple Lie superalgebras and their universal \(R\)-matrices, Graded PI-exponents of simple Lie superalgebras, Unitary highest weight representations of quantum general linear superalgebra, On charge conjugation, The finite-dimensional modular Lie superalgebra \(\Omega \), Duality property in coinduced representations of Lie superalgebras, Finite-dimensional representations of the quantum superalgebra \(U_ q[gl(n/m)\) and related \(q\)-identities], Hypergroups and hypergroup algebras, Two families of flag supermanifolds, Fractal nil graded Lie superalgebras, Integral bases for the universal enveloping algebras of Cartan map superalgebras, Diamond cone for \(\mathfrak{spo}(2m, 1)\), LYM inequalities for \(t\)-antichains, Representations and cocycle twists of color Lie algebras, Lie superalgebras, Clifford algebras, induced modules and nilpotent orbits, Representation of Lie superalgebras and generalized boson-fermion equivalence in quantum stochastic calculus, Generalized \(B(m,n)\), \(C(n)\), \(D(m,n)\)-graded Lie superalgebras arising from fermionic-bosonic representations, Gauge theories, flat superforms and reduction of super fiber bundles, Subalgebras of free Lie p-superalgebras, Identities of solvable color Lie superalgebras, Combinatorics, transvectants and superalgebras. An elementary constructive approach to Hilbert's finiteness theorem, Some deformations of nilpotent Lie superalgebras, Non-matrix polynomial identity enveloping algebras, Gradings, braidings, representations, paraparticles: some open problems, Maximal subalgebras of Lie superalgebras of Cartan type over fields of characteristic zero, Singular quadratic Lie superalgebras, Infinitesimal deformations of filiform Lie algebras of order 3, Classification of maximal transitive prolongations of super-Poincaré algebras, Representations of the restricted Cartan type Lie superalgebra \(W(m,n,1)\), On natural superhomogeneous models for Minkowski superspacetime, On the modular Lie superalgebra \(\varOmega \), On holomorphic functions on a compact complex homogeneous supermanifold, On cohomology and support varieties for Lie superalgebras, Extended affine root supersystems, Invariant operators on geometric quantities, The Dixmier map for nilpotent super Lie algebras, Supercharacters and superdimensions of irreducible representations of B(O/s) orthosymplectic simple Lie superalgebras, A remarkable connection between the representations of the Lie superalgebras osp(1,2n) and the Lie algebras o(2n+1), Heisenberg Lie superalgebras and their invariant superorthogonal and supersymplectic forms, Derivations of the even part of contact Lie superalgebra, A construction of Lie-graded algebras by graded generalized Jordan triples of second order, The supergroups of supersymmetry and supergravity as ordinary real Lie groups, Graded identities of some simple Lie superalgebras, Graded codimensions of Lie superalgebra \(b(2)\), Infinitesimal deformations of the Lie superalgebra \(L^{n,m}\), Orthosymplectic Lie superalgebras in superspace analogues of quantum Kepler problems, Representations of quantum affine superalgebras, Finite-dimensional irreducible representations of the quantum superalgebra \(U_ q[gl(n/1)\)], Free fermions and the Alexander-Conway polynomial, Lie supergroups obtained from 3-dimensional Lie superalgebras associated to the adjoint representation and having a 2-dimensional derived ideal, The massless string spectrum on \(\mathrm{AdS}_{3}\times S^{3}\) from the supergroup, Engel condition on enveloping algebras of Lie superalgebras, Structural theory of special Lie algebras, On the ring extensions arising from completely solvable Lie superalgebras, Metasymmetry and Volichenko algebras, Riemannian supergeometry, On the weight spaces of Lie superalgebra modules, A classification of primitive ideals in the enveloping algebra of a classical simple Lie superalgebra, Projective uniformization and graded Lie algebras over Riemann surfaces, The first fundamental theorem of invariant theory for the orthosymplectic supergroup, Structure constants for the \(\text{osp}(1|2)\) current algebra, Pauli gradings on Lie superalgebras and graded codimension growth, Fermionic and supersymmetric stochastic processes, A Darboux transformation of the \(\mathrm{sl}(2| 1)\) super KdV hierarchy and a super lattice potential KdV equation, True BRST symmetry algebra and the theory of its representations, On complex Lie supergroups and split homogeneous supermanifolds, On the generators of Lie superalgebras, Quantum field theory on a discrete space and noncommutative geometry, Modular Lie superalgebras of \(H\)-type, Some problems concerning to nilpotent Lie superalgebras, Superization of homogeneous spin manifolds and geometry of homogeneous supermanifolds, ARI/GARI, dimorphy and multiple zeta arithmetic: a first evaluation, On a Regev-Seeman conjecture about \(\mathbb{Z}_2\)-graded tensor products., Deformations of filiform Lie algebras and superalgebras, A universal enveloping algebra of Malcev superalgebras, Infinite-dimensional Hamiltonian Lie superalgebras, Double extensions of Lie superalgebras in characteristic 2 with nondegenerate invariant supersymmetric bilinear form, Affine quotients of supergroups, Quadratic Lie superalgebras with a reductive even part, On the simple modules for the restricted Lie superalgebra \(\text{sl}(n|1)\), Non-integrality of the PI-exponent of special Lie algebras, Quadratic symplectic Lie superalgebras and Lie bi-superalgebras, Polynomial identities for graded tensor products of algebras., Graded Lie superalgebras and the superdimension formula, The Lie algebraic structure of differential operators admitting invariant spaces of polynomials, A criterion for primeness of enveloping algebras of Lie superalgebras, Embedding theorem of \(\mathbb Z\)-graded Lie superalgebras, Intermediate growth of solvable Lie superalgebras, Bell's primeness criterion and the simple Lie superalgebras, A complete description of all the infinitesimal deformations of the Lie superalgebra \(L^{n,m}\), The fuzzy supersphere, Lie superalgebras, infinite-dimensional algebras and quantum statistics, Introduction to Poisson supermanifolds, On current superalgebras and super-Schwinger terms, Borel-Weil-Bott theory for classical Lie superalgebras, On the primary decomposition theorem of modular Lie superalgebras, Dissections and automorphisms of regular Courant algebroids, New simple Lie superalgebras in characteristic 3, First-order intertwining operators and position-dependent mass Schrödinger equations in \(d\) dimensions, Quantum superalgebra representations on cohomology groups of non-commutative bundles, Color Lie rings and PBW deformations of skew group algebras, Constructing \(R\)-matrices on simple Lie superalgebras, Generalised Jantzen filtration of exceptional Lie superalgebras, Group gradings on the superalgebras \(M(m,n)\), \(A(m,n)\) and \(P(n)\), Some remarks on solvable Lie superalgebras, Fractal just infinite nil Lie superalgebra of finite width, Simplicities of VOAs associated to Jordan algebras of type \(B\) and character formulas for simple quotients, Odd-quadratic Lie superalgebras with a weak filiform module as an odd part, On the center of the enveloping algebra of a classical simple Lie superalgebra, Supercoherent states, super-Kähler geometry and geometric quantization, Symbolic superalgebra manipulations using COMMON LISP, Fusion rules and singular vectors of the \(\text{osp}(1|2)\) current algebra, A generalized non-isospectral super AKNS hierarchy associated with the orthosymplectic Lie superalgebra \(osp(2, 2)\), Constructing simple Lie superalgebras from associative graded algebras, Jordan-Lie super algebra and Jordan-Lie triple system, Color Lie superalgebras and Hopf algebras, A new integrable symplectic map by the binary nonlinearization to the super AKNS system, Varieties of nilpotent Lie superalgebras of dimension \(\leq 5\), Symmetry transformations with noncommutative and nonassociative parameters, Generalizations of Lie algebras, Good gradings of basic Lie superalgebras, The Harish-Chandra isomorphism for reductive symmetric superpairs, Super-biderivations of classical simple Lie superalgebras, Solvable Lie and Leibniz superalgebras with a given nilradical, A determinantal formula for supersymmetric Schur polynomials, Invariant forms of the elementary unitary Lie superalgebra., On the second fundamental theorem of invariant theory for the orthosymplectic supergroup, Lie superalgebras based on \(\mathfrak{gl}_n\) associated to the adjoint representation, and invariant geometric structures defined on them, On a class of algebras defined by partitions., On matrix realizations of the Lie superalgebra \(D(2,1;\alpha )\), On cohomology of the Lie superalgebra \(D(2,1;\alpha )\), Quadratic Malcev superalgebras., The derivation algebra of the Cartan-type Lie superalgebra \(HO\)., A new definition of restricted Lie superalgebras, Double extensions of Lie algebras of Kac-Moody type and applications to some Hamiltonian systems, \(\text{gl}(N,N)\) current algebras and topological field theories, Quadratic Lie superalgebras with the completely reducible action of the even part of the odd part, Quadratic Lie superalgebras generalized by Balinsky-Novikov superalgebras, A family of transitive modular Lie superalgebras with depth one, Gauss decomposition of the Yangian \(Y({\mathfrak{gl}}_{m|n})\), On Killing forms and invariant forms of Lie-Yamaguti superalgebras, A super-analogue of Kontsevich's theorem on graph homology, Singular degenerations of Lie supergroups of type \(D(2,1;a)\), Fractal nil graded Lie, associative, Poisson, and Jordan superalgebras, On Jordan doubles of slow growth of Lie superalgebras, Generalised Verma modules for the orthosymplectic Lie superalgebra \(\mathfrak {osp}_{k|2}\), Weyl modules and Weyl functors for Lie superalgebras, Jeu de taquin and diamond cone for Lie (super)algebras, A class of generalized odd Hamiltonian Lie superalgebras, Omni-Lie superalgebras and Lie 2-superalgebras, On naturally graded Lie and Leibniz superalgebras, Odd-quadratic Leibniz superalgebras, Unipotent algebraic affine supergroups and nilpotent Lie superalgebras., Odd-quadratic Lie superalgebras, Superizations of Cahen-Wallach symmetric spaces and spin representations of the Heisenberg algebra, Cohomology and support varieties for restricted Lie superalgebras, Infinite-dimensional modular special odd contact superalgebras, Chevalley's restriction theorem for reductive symmetric superpairs, The general and special superalgebras of formal vectorfields, Lie supergroups supported over \(\text{GL}_2\) and \(\text{U}_2\) associated to the adjoint representation, Necklace rings and logarithmic functions, The Frattini subalgebra of restricted Lie superalgebras, Fundamental fermions fit inside one \(\text{su}(1|5)\) irreducible representation, Enveloping Lie superalgebras and Killing-Ricci forms of Bol superalgebras, The Capelli eigenvalue problem for Lie superalgebras, String states on \(\mathrm{AdS}_3\times S^3\) from the supergroup, Character and dimension formulae for queer Lie superalgebra, Non-abelian tensor product and homology of Lie superalgebras, Mixed cohomology of Lie superalgebras, Parabolic subalgebras and gradings of reductive Lie superalgebras, Classification of infinite dimensional irreducible modules for type I Lie superalgebras, The umbral symbolic method for supersymmetric tensors, On low-dimensional complex \(\omega \)-Lie superalgebras, Constructions and properties for a finite-dimensional modular Lie superalgebra \(K(n, m)\), Structure of sympathetic Lie superalgebras, Some results concerning the multiplicities of cocharacters of superalgebras with graded involution, Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras, \(\mathbb Z\)-graded Lie superalgebras with depth one over fields of prime characteristic., The natural filtration of finite dimensional modular Lie superalgebras of special type, Infinite-dimensional modular Lie superalgebra \(\Omega\), Graded parafermions, Dualisation of dualities. II: Twisted self-duality of doubled fields and superdualities., On cohomologies and algebraic \(K\)-theory of Lie \(p\)-superalgebras, Cohomology of Dowling lattices and Lie (super)algebras, On the Goldie quotient ring of the enveloping algebra of a classical simple Lie superalgebra, \(\mathbb{Z}_2\)-graded tensor products of p.i. algebras., Integration on Lie supergroups: a Hopf superalgebra approach, Natural filtrations of infinite-dimensional modular contact superalgebras, On the compatibility of \(\mathbb Z\)- and \(\mathbb Z_2\)-gradations at ``strange Lie superalgebras \(P(N)\) pointed out by the Jacobi identity, Some results on complete Lie superalgebras, On endotrivial modules for Lie superalgebras, The general linear supergroup and its Hopf superalgebra of regular functions., Classification of finite simple Lie conformal superalgebras., Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras, Modular representations of the supergroup \(Q(n)\). I, Socle and some invariants of quadratic Lie superalgebras, QUASI-CLASSICAL LIE SUPERALGEBRAS AND LIE SUPERTRIPLE SYSTEMS, Infinite-Dimensional Modular Odd Hamiltonian Superalgebras, Derivation Algebra Der(H) and Central Extensions of Lie Superalgebras, Associative Superalgebras with Homogeneous Symmetric Structures, COMPOSITION SUPERALGEBRAS, A Class of Finite-dimensional Lie Superalgebras of Hamiltonian Type, Infinite-dimensional Modular Lie Superalgebras W and S of Cartan Type, Solvability of Finite-Dimensionaln-ary Commutative Leibniz Algebras of Characteristic 0, Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups, On indecomposable solvable Lie superalgebras having a Heisenberg nilradical, On the Construction of Chevalley Supergroups, A note on semiprime Malcev superalgebras, FINITE-DIMENSIONAL HAMILTONIAN LIE SUPERALGEBRA, Prime ideals in finite extensions of Noetherian rings, Relative cohomology spaces for some osp(n|2)-modules, Invariant bilinear forms on Leibniz superalgebras, Classification of real Lie superalgebras based on a simple Lie algebra, giving rise to interesting examples involving ${\mathfrak {su}}(2,2)$su(2,2), Lie superalgebras based on Heisenberg Lie algebras, On the Intersection of Maximal Subalgebras in a Lie Superalgebra, Unnamed Item, Some properties of the family Γ of modular Lie superalgebras, Finite-dimensional Lie algebras of order F, 2-Local superderivations on the deformative super W-algebras Wλs(2,2), PBW degenerations of Lie superalgebras and their typical representations, TYPICAL BLOCKS OF THE CATEGORY $\mathcal{O}$ FOR THE QUEER LIE SUPERALGEBRA, Construction of color Lie algebras from homomorphisms of modules of Lie algebras, Simply complete Hom-Lie superalgebras and decomposition of complete Hom-Lie superalgebras, A Schr\"odinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra $D(2,1;\alpha)$, Reduced Wigner coefficients for Lie superalgebragl(m|n) corresponding to unitary representations and beyond, On classical tensor categories attached to the irreducible representations of the general linear supergroups \(GL(n|n)\), Super-biderivations and linear super-commuting maps on the Lie superalgebras, On the action of the Koszul map on the enveloping algebra of the general linear Lie algebra, Automorphism groups of modular graded Lie superalgebras of Cartan-type, Spanning forests andOSP(N|2M) -invariantσ-models, On constructions of Lie (super) algebras and (𝜀,δ)-Freudenthal–Kantor triple systems defined by bilinear forms, DERIVATIONS OF THE EVEN PARTS FOR MODULAR LIE SUPERALGEBRAS OF CARTAN TYPE W AND S, A supertrace identity and its applications to superintegrable systems, Quadratic Color Hom-Lie Algebras, Identities for Lie superalgebras with a nilpotent commutator subalgebra, Simple supermodules over Lie superalgebras, Unnamed Item, Reflection matrices for theUq[spo(2n|2m) vertex model], Unnamed Item, Bell's Primeness Criterion for W(2n + 1), Second cohomology of q-deformed Witt superalgebras, On supersymmetric eigenvectors of the 5D discrete Fourier transform, On structure and TKK algebras for Jordan superalgebras, Unnamed Item, Cohomology of Hom-Lie superalgebras and q-deformed Witt superalgebra, Primeness of the enveloping algebra of Hamiltonian superalgebras, ON SOME LEFT-SYMMETRIC SUPERALGEBRAS, Codimension growth of solvable Lie superalgebras, Non-degenerate Invariant Bilinear Forms on Lie Color Algebras, The Finite-dimensional Modular Lie Superalgebra Γ, Filiform Lie algebras of order 3, A braided monoidal category for free super-bosons, A STRUCTURE THEORY OF (−1,−1)-FREUDENTHAL KANTOR TRIPLE SYSTEMS, Classical Lie Supergroups, Generalized Derivations of Lie Superalgebras, The Cartan-Type Modular Lie SuperalgebraKO, On degenerations of Lie superalgebras, On Right Alternative Superalgebras, Moduli spaces of low-dimensional Lie superalgebras, The minimal number of generators for finite-dimensional Cartan Lie superalgebras, Complete hom-Lie superalgebras, Schur 𝑄-functions and the Capelli eigenvalue problem for the Lie superalgebra \ger𝑞(𝑛), Root Supermultiplicities of Some Borcherds Superalgebras, The Outer Derivation Algebras of Finite-Dimensional Cartan-Type Modular Lie Superalgebras, On principal finite W-algebras for the Lie superalgebra D(2, 1; α), A CHARACTERIZATION OF (−1, −1)-FREUDENTHAL–KANTOR TRIPLE SYSTEMS, Lie Superalgebras Over 𝔤𝔩2, Triple products on n, FINITE-DIMENSIONAL SPECIAL ODD HAMILTONIAN SUPERALGEBRAS IN PRIME CHARACTERISTIC, Classification of finite-dimensional Lie superalgebras whose even part is a three-dimensional simple Lie algebra over a field of characteristic not two or three, A construction of simple Lie subalgebras of certain types from triple systems, FINE GRADINGS ON EXCEPTIONAL SIMPLE LIE SUPERALGEBRAS, Solvable Pseudo-Euclidean Jordan Superalgebras, Cohomological Tensor Functors on Representations of the General Linear Supergroup, Ad-Nilpotent Elements, Isomorphisms, and the Weisfeiler Filtration of Infinite-Dimensional Modular Odd Contact Superalgebras, Maximal subalgebras for Lie superalgebras of Cartan type, Supercommutator (Hom-)superalgebras of right (Hom-)alternative superalgebras, Young–Capelli bitableaux, Capelli immanants in U(gl(n)) and the Okounkov quantum immanants, The spaces Hn(osp(1∣2),M) for some modules M, Gel’fand–Zetlin basis and Clebsch–Gordan coefficients for covariant representations of the Lie superalgebra gl(m∣n), The Next Step Beyond Graded Lie Algebra: Recoupling Lie Algebra, On δ-Lie supertriple systems associated with (ε, δ)-Freudenthal-Kantor supertriple systems, Automorphism Groups of Restricted Cartan-Type Lie Superalgebras, Cohomology of Lie superalgebras 𝔰𝔩m|nand 𝔬𝔰𝔭2|2n, Quadratic (resp. symmetric) Leibniz superalgebras, Super-biderivations of Cartan type Lie superalgebras, Cohomologically rigid solvable Lie superalgebras with model filiform and model nilpotent nilradical, 2-Local superderivations on the super Virasoro algebra and the super W(2,2) algebra, A Review of Peirce Decomposition for Unitary $$(-1,-1)$$-Freudenthal Kantor Triple Systems, Malcev superalgebras with trival nucleus, A NONASSOCIATIVE QUATERNION SCALAR FIELD THEORY, ON SUPERMULTIPLET TWISTING AND SPIN-STATISTICS, Low-dimensional commutative power-associative superalgebras, Exact sequences in the cohomology of a Lie superalgebra extension, Leibniz central extensions of Lie superalgebras, Local superderivations on Cartan type Lie superalgebras, 2-Local Automorphisms on Basic Classical Lie Superalgebras, Quadratic symplectic Lie superalgebras with a filiform module as an odd part, Quantum immanants, double Young–Capelli bitableaux and Schur shifted symmetric functions, On certain algebraic structures associated with Lie (super)algebras, Capelli-Deruyts bitableaux and the classical Capelli generators of the center of the enveloping algebra U( gl ( n )), Characterization of contact Lie superalgebras, Orthosymplectic Z2×Z2Z2×Z2 -graded Lie superalgebras and parastatistics, Nilpotent inner derivations in prime superalgebras, Unnamed Item, Unnamed Item, Quantum divided power algebra, \(q\)-derivatives, and some new quantum groups, Primeness criteria for universal enveloping algebras of Lie color algebras, Lie superalgebras, Representations of Lie colour algebras, A straightening algorithm for row-convex tableaux, A class of finite dimensional modular Lie superalgebras of special type, Indecomposable doubling for representations of the type I Lie superalgebras sl(m/n) and osp(2/2n)
