Noncommutative algebra and representation theory: symmetry, structure \& invariants

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Ordinary and skew polynomial rings and semigroup rings (16S36) Rings of differential operators (associative algebraic aspects) (16S32)

Cites Work

The classification of $n$-dimensional non-Lie Malcev algebras with $(n-4)$-dimensional annihilator
An alternate approach to the Lie bracket on Hochschild cohomology
From quantum Ore extensions to quantum tori via noncommutative UFDs
On normal subgroups of $\Aut_k(A_1(k))$, the $k$-automorphisms group of Weyl algebra $A_1(k)$.
Hopf subalgebras and tensor powers of generalized permutation modules.
On the cohomology of the Weyl algebra, the quantum plane, and the $q$-Weyl algebra.
Classification of factorial generalized down-up algebras.
Generalized Heisenberg algebra coherent states for power-law potentials
On the $q$-meromorphic Weyl algebra.
The Jordan plane over a field of positive characteristic.
Frobenius algebras. I: Basic representation theory.
Combinatorial models of creation-annihilation
Double extension regular algebras of type (14641).
Twisted Calabi-Yau property of Ore extensions.
Factorial properties of the enveloping algebra of a nilpotent Lie algebra in prime characteristic
Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
Double Ore extensions.
A q-difference analogue of $U({\mathfrak g})$ and the Yang-Baxter equation
The algebraic and geometric classification of associative algebras of dimension five
The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra
Finite dimensionality of $\text{Ext}^ n$'s and $\text{Tor}_ n$'s of simple modules over one class of algebras
On the varieties of nilpotent Lie algebras of dimension 7 and 8
Classification of Harish-Chandra modules over the Virasoro Lie algebra
Primitive ideals in enveloping algebras
$q$-analogs of harmonic oscillators and related rings
Down-up algebras
Duality of graded graphs
On the center of $U_ q({\mathfrak n}^ +)$
On the field of fractions of certain quantum algebras
$q$-Gaussian processes: Non-commutative and classical aspects
The simple modules of certain generalized crossed products
$q$-difference equations.
Down-up algebras and their representation theory
Lectures on algebraic quantum groups
A quantum subgroup depth
A little bit of extra functoriality for Ext and the computation of the Gerstenhaber bracket
Vanishing of derivations and prime spectra of quantum algebras
Basic properties of generalized down-up algebras.
Study of the $q$-commutations in the algebra $U_ q(n^ +)$
Noncommutative graded domains with quadratic growth
Normally ordered forms of powers of differential operators and their combinatorics
The algebraic and geometric classification of nilpotent anticommutative algebras
Lie structure on the Hochschild cohomology of a family of subalgebras of the Weyl algebra
Non-associative central extensions of null-filiform associative algebras
Quantum Weyl algebras and reflection equation algebras at a root of unity
Actions of the additive group $G_a$ on certain noncommutative deformations of the plane
On deformations of complex analytic structures. II
Upper bounds for the length of non-associative algebras
Simple weight modules over weak generalized Weyl algebras.
Finite-dimensional simple modules over generalized Heisenberg algebras
Automorphisms and derivations of $U_q(\mathfrak{sl}^+_4)$
Endomorphisms of Weyl algebra and $p$-curvatures.
Central extensions of null-filiform and naturally graded filiform non-Lie Leibniz algebras
Rigidity of quantum tori and the Andruskiewitsch-Dumas conjecture
The first Hochschild cohomology group of quantum matrices and the quantum special linear group.
Derivations of a parametric family of subalgebras of the Weyl algebra.
Algebraic geography: Varieties of structure constants
Quotients simples de l'algèbre enveloppante de ${\mathfrak sl}_2$
Über ganze birationale Transformationen der Ebene.
Éléments de géométrie algébrique. I: Le langage des schémas. II: Étude globale élémentaire de quelques classe de morphismes. III: Étude cohomologique des faisceaux cohérents (première partie)
On the deformation of rings and algebras
A multiparameter family of irreducible representations of the quantum plane and of the quantum Weyl algebra.
Noncommutative Noetherian rings. With the cooperation of L. W. Small.
Multi-parametric deformed Heisenberg algebras: a route to complexity
Commutation Relations, Normal Ordering, and Stirling Numbers
Non-Noetherian generalized Heisenberg algebras
Introduction to representation theory
Double Ore Extensions Versus Iterated Ore Extensions
Some remarks about the derivative operator and generalized Stirling numbers
Non-commutative unique factorization domains
A Class of Algebras Similar to the Enveloping Algebra of sl(2)
Separation of Variables for
Primitive Ideals of
PRIMITIVE IDEALS AND AUTOMORPHISM GROUP OF $U_{q}^{+}(B_{2})$
Automorphisms of Generalized Down-Up Algebras
Hopf quivers and Nichols algebras in positive characteristic
2-Nilpotent and Rigid Finite Dimensional Algebras
Non-Commutative Unique Factorisation Rings
Un automorphisme non modéré deU(g₃)
Differential Posets
Representations of $\mathfrak{sl}( 2,\mathbb{C} )$ on Posets and the Sperner Property
Derivations et automorphismes de quelques algebras quantiques
On algebraically irreducible representations of the Lie algebra sl(2)
Algèbres d'opérateurs différentiels et quotients des algèbres enveloppantes
A wild automorphism ofUsl(2)
The simple modules of the ore extensions with coefficients from a dedekind ring
Noetherian down-up algebras
Separation of Variables for Quantized Enveloping Algebras
Examples in non-commutative projective geometry
Conformal S1₂ enveloping algebras
A relation between Hochschild homology and cohomology for Gorenstein rings
The tame and the wild automorphisms of polynomial rings in three variables
Isomorphism problems and groups of automorphisms for generalized Weyl algebras
SOME ALGEBRAS SIMILAR TO THE ENVELOPING ALGEBRA OF sl(2)
Generalized Heisenberg algebra and (non linear) pseudo-bosons
Exact solution of a 1D asymmetric exclusion model using a matrix formulation
Endomorphisms of Right Ideals of the Weyl Algebra
Gerstenhaber Bracket on the Hochschild Cohomology via An Arbitrary Resolution
A Parametric Family of Subalgebras of the Weyl Algebra II. Irreducible Modules
The algebraic classification of nilpotent algebras
Quantum generalized Heisenberg algebras and their representations
On automorphisms of Weyl algebra
Hochschild Cohomology for Algebras
Rigidité des plongements des quotients primitifs minimaux de U_g(sl(2)) dans l’algebre quantique de Weyl-Hayashi
Lie Group Representations on Polynomial Rings
Representation Spaces of the Jordan Plane
A parametric family of subalgebras of the Weyl algebra I. Structure and automorphisms
Cohomology and deformations in graded Lie algebras
Sur les algèbres de Weyl
Unique Factorization Domains
Structure and isomorphisms of quantum generalized Heisenberg algebras
Derivations of skew polynomial rings
The geometric classification of nilpotent algebras
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