Lie groups

DOI10.1007/BF02105458zbMath0566.22001OpenAlexW4211014722WikidataQ115392768 ScholiaQ115392768MaRDI QIDQ5902752

Dimitrii V. Alekseevsky

Publication date: 1985

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02105458

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) General properties and structure of real Lie groups (22E15) Research exposition (monographs, survey articles) pertaining to topological groups (22-02) Noncompact Lie groups of transformations (57S20)

Cites Work

• Observable subgroups of a complex semisimple Lie group
• On invariant measures, minimal sets and a lemma of Margulis
• On unitary automorphisms of solvable Lie algebras
• On representing analytic groups with their automorphisms
• Selection of subspaces with special properties in a Banach space and some properties of quasicomplements
• Quasiclans
• A note on the Campbell-Hausdorff formula
• Best linear and nonlinear approximations for smooth functions
• On a class of type I solvable Lie groups. II
• Arithmetic groups
• Les orbites d'un espace hermitien symétrique compact
• Asymptotic behavior of multiplicities of representations of compact groups
• Some remarks on nilpotent orbits
• A simple proof of Borel's density theorem
• Closures of conjugacy classes of matrices are normal
• On the exponential map in classical Lie groups
• Transitivitätsfragen bei linearen Liegruppen
• A geometric proof of the conjugacy of Borel and Cartan subalgebras of the classical simple Lie algebras
• Goldie rank in the enveloping algebra of a semisimple Lie algebra. I, II
• Groups of automorphisms of Lie groups: Density properties, bounded orbits, and homogeneous spaces of finite volume
• A generalization of the Chevalley restriction theorem
• Characters of the nullcone
• Orbits on affine symmetric spaces under the action of the isotropy subgroups
• Immersions of Lie groups
• Invariant convex cones and orderings in Lie groups
• Ideaux primitifs des algèbres enveloppantes
• On a remarkable class of polyhedra in complex hyperbolic space
• Orbits of Euclidean frames under discrete linear groups
• Über den Symmetriegrad der rational azyklischen kompakten homogenen Räume
• Harmonic analysis on reductive Lie groups
• Invariant convex cones and causality in semisimple Lie algebras and groups
• Minimal singularities in \(GL_ n\).
• Simple singularities and infinitesimally symmetric spaces
• Suites de Jordan-Hölder et principales d'un groupe de Lie
• Deformations of bouquets of quasihomogeneous one-dimensional singularities
• Simplified descriptions of the exceptional bounded symmetric domains
• On a ring of invariant polynomials on a Hermitian symmetric space
• La représentation coadjointe du groupe affine
• Cohomology of infinite-dimensional Lie algebras and characteristic classes of foliations
• Sous-groupes conjugues d'un groupe linéaire
• Sur la théorie des invariants des groupes classiques
• Fonctions différentiables invariantes sous l'opération d'un groupe réductif
• Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie- Algebra
• Modular forms and root systems
• Surjectivity of exponential map on semisimple Lie groups
• Étude de la 1-cohomologie et de la topologie du dual pour les groupes de Lie à radical abelien
• On density properties of certain subgroups of locally compact groups
• On Macdonald's \(\eta\)-function formula, the Laplacian and generalized exponents
• A remark on a question of Margulis
• Affine open orbits, reductive isotropy groups, and dominant gradient morphisms; a theorem of Mikio Sato
• Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple
• Primitive vollprime Ideale in der Einhüllenden von \(\mathfrak {so}(5,\mathbb{C})\)
• Definition einer Dixmier-Abbildung für \(\mathfrak{sl}(n,\mathbb C)\)
• Higher order contact of submanifolds of homogeneous spaces
• Compact Euclidean space forms
• Jordan algebras and symmetric Siegel domains in Banach spaces
• Parametrisierung von Konjugationsklassen in \(\mathfrak {sl}_n\)
• Relative Invarianten und nichtassoziative Algebren
• Sur la théorie classique des invariants
• Polarizations in the classical groups
• Horispherical subalgebras of real Lie algebras
• Primitive ideals in enveloping algebras
• Über die unipotenten Klassen reduktiver Gruppen
• Addendum to ``Fixed points of automorphisms of compact Lie groups
• Präsentation der Einheitengruppe der quadratischen Form \(F(X)=- X^2_0+X^2_1+\ldots+X^2_{18}\)
• Dense orbits in Z(P) the singular hypersurface of a prehomogeneous vector space
• The intersection pairing on a homogeneous Kähler manifold
• On multiplicity in the Jordan-Hölder series of Verma modules
• Generalized Verma modules, the Cartan-Helgason theorem, and the Harish- Chandra homomorphism
• On the density theorems of Borel und Furstenberg
• On \(L\)-subgroups of locally compact groups
• Filtrations and asymptotic automorphisms on nilpotent Lie groups
• Representations of simple Lie groups with regular rings of invariants
• Some remarks on automorphisms of bounded displacement and bounded cocycles
• Über Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen
• The normality of closures of orbits in a Lie algebra
• Über Automorphismenbahnen von Elementen \(u\neq 0\) mit \((ad\;u)^3=\alpha\;ad\;u\) in endlichdimensionalen einfachen komplexen Lie- Algebren
• The orbits of affine symmetric spaces under the action of minimal parabolic subgroups
• Harmonic analysis on compact solvmanifolds
• Some remarks suggesting an interesting theory of harmonic functions on SU(2n+1)/Sp(n) and SO(2n+1)/U(n)
• Conjugacy in a semisimple Lie algebra is determined by similarity under fundamental representations
• A preparation theorem for the prime spectrum of a semisimple Lie algebra
• Regularly related lattices in Lie groups
• On Whittaker vectors and representation theory
• Remarques sur un article de J. W. Robbin
• La déformation des formes hermitiennes et son application aux domaines de Siegel
• Invariants in enveloping algebras under the action of Lie algebras of derivations
• On frobenius lie algebras
• On the structure of solvable Lie algebras.
• Inductive Construction of Homogeneous Cones
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• Casimir invariants and vector operators in simple and classical Lie algebras
• Operator Siegel Domains
• Exponential Map and Automorphism Group of a Connected Lie Group
• Conjugacy Classes in Parabolic Subgroups of Semisimple Algebraic Groups, II
• Second Commutant Theorems in Enveloping Algebras
• Invariant differential equations on homogeneous manifolds
• Integral Invariant Functions on the Nilpotent Elements of a Semisimple Lie Algebra
• The Cohomology of Semisimple Lie Algebras with Coefficients in a Verma Module
• An algorithm for generating dominant weights
• On tensor operators and characteristic identities for semi-simple Lie algebras
• Exceptional Lie algebras and the structure of Hermitian symmetric spaces
• The Classification of Flat Solvmanifolds
• Gelfand-Kirillov Dimension for the Annihilators of Simple Quotients of Verma Modules
• Existence of a nonarithmetic lattice in SU (2,1)
• Principal Irreducible Lie-Algebra Modules
• Dense Subgroups of Lie Groups. II
• On the Existence of Dense Analytic Subgroups
• Naturally reductive metrics and Einstein metrics on compact Lie groups
• On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case
• Champs de vecteurs adjoints sur les groupes et algèbres de Lie semi-simples.
• The characteristic identities and reduced matrix elements of the unitary and orthogonal groups
• Quartic trace identity for exceptional Lie algebras
• Matrix groups
• Generalized symmetric spaces
• Riemann surfaces
• Linear groups
• Horizontal \(SL_2\)-orbits in flag domains
• Dilations and gauges on nilpotent Lie groups
• A Simple Expression for the Casimir Operator on a Lie Group
• Quasisymmetric Siegel Domains and the Automorphisms of Homogeneous Siegel Domains
• Automorphisms of Siegel Domains
• S-Subgroups of the Real Hyperbolic Groups
• Reduced determinantal forms for characters of the classical Lie groups
• Dimensions of irreducible representations of the classical Lie groups
• An analogue of the Mostow-Margulis rigidity theorems for ergodic actions of semisimple Lie groups
• Algèbres de Lie métabéliennes
• On nth roots and infinitely divisible elements in a connected Lie group
• The Weyl groups and weight multiplicities of the exceptional Lie groups
• Kronecker products of representations of exceptional Lie groups
• THE TOPOLOGICAL STRUCTURE OF COMPACT HOMOGENEOUS MANIFOLDS
• Dynamics of horospherical flows
• GELFAND-KIRILLOV DIMENSION IN ENVELOPING ALGEBRAS
• Young–tableau methods for Kronecker products of representations of the classical groups
• A unipotent group associated with certain linear groups
• On a class of homogeneous spaces of compact Lie groups
• Ideals of Coadjoint Orbits of Nilpotent Lie Algebras
• Compactness of Certain Homogeneous Spaces of Locally Compact Groups
• A Note on Borel's Density Theorem
• A classification of irreducible prehomogeneous vector spaces and their relative invariants
• A Generalization of H. Weyl's "Unitary Trick"
• On Torsion Subgroups of Lie Groups
• Singularities in the Nilpotent Scheme of a Classical Group
• On classification of quasi-symmetric domains
• On the Singularity of the Exponential Map on a Lie Group
• Polarisation dans les algèbres de Lie. II
• Filtrations and Canonical Coordinates on Nilpotent Lie Groups
• Discrete Subgroups Isomorphic to Lattices in Semisimple Lie Groups
• Homogeneous Spaces with Finite Invariant Measure
• A Simple Subgroup of M ? and E ₈ (3)
• Exceptional Lie Algebras and Related Algebraic and Geometric Structures
• A Characteristically Nilpotent Lie Algebra Can be a Derived Algebra
• On Relatively Free Subsets of Lie Groups
• Closure Theorem for Analytic Subgroups of Real Lie Groups
• Homogeneous manifolds with negative curvature. II
• Discrete Subgroups Isomorphic to Lattices in Lie Groups
• A Characterization of Unipotent, Semisimple and Regular Elements in a Reductive Algebraic Group
• On the embedding of the Cayley plane into the exceptional Lie group of type $F_{4}$
• Distal affine transformation groups.
• A Family of Lie Algebras not Extendible to a Family of Lie Groups

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