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Displaying 41 – 60 of 182

Enveloping algebras of Slodowy slices and the Joseph ideal

Alexander Premet (2007)

Journal of the European Mathematical Society

Let $G$ be a simple algebraic group over an algebraically closed field $𝕜$ of characteristic 0, and $𝔤 = Lie G$ . Let $(e, h, f)$ be an $𝔰 𝔩_{2}$ -triple in $𝔤$ with $e$ being a long root vector in $𝔤$ . Let $(\cdot, \cdot)$ be the $G$ -invariant bilinear form on $𝔤$ with $(e, f) = 1$ and let $χ \in 𝔤^{*}$ be such that $χ (x) = (e, x)$ for all $x \in 𝔤$ . Let $𝒮$ be the Slodowy slice at $e$ through the adjoint orbit of $e$ and let $H$ be the enveloping algebra of $𝒮$ ; see [31]. In this article we give an explicit presentation of $H$ by generators and relations. As a consequence we deduce that $H$ contains an ideal...

Equivariant deformation quantization for the cotangent bundle of a flag manifold

Ranee Brylinski (2002)

Annales de l’institut Fourier

Let $X$ be a (generalized) flag manifold of a complex semisimple Lie group $G$ . We investigate the problem of constructing a graded star product on $ℛ = R (T^{☆} X)$ which corresponds to a $G$ -equivariant quantization of symbols into twisted differential operators acting on half-forms on $X$ . We construct, when $ℛ$ is generated by the momentum functions $μ^{x}$ for $G$ , a preferred choice of $☆$ where $μ^{x} ☆ φ$ has the form $μ^{x} φ + \frac{1}{2} {μ^{x}, φ} t + Λ^{x} (φ) t^{2}$ . Here $Λ^{x}$ are operators on $ℛ$ . In the known examples, $Λ^{x}$ ( $x \neq 0$ ) is not a differential operator, and so the star product $μ^{x} ☆ φ$ ...

Euclidean components for a class of self-injective algebras

Sarah Scherotzke (2009)

Colloquium Mathematicae

We determine the length of composition series of projective modules of G-transitive algebras with an Auslander-Reiten component of Euclidean tree class. We thereby correct and generalize a result of Farnsteiner [Math. Nachr. 202 (1999)]. Furthermore we show that modules with certain length of composition series are periodic. We apply these results to G-transitive blocks of the universal enveloping algebras of restricted p-Lie algebras and prove that G-transitive principal blocks only allow components...

Exact Borel subalgebras of quasi-heriditary algebras, I (with an appendix by Leonard Scott).

Steffen König (1995)

Mathematische Zeitschrift

Fair-sized projective modules

Pavel Příhoda (2010)

Rendiconti del Seminario Matematico della Università di Padova

Family algebras.

Kirillov, A.A. (2000)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Filtrations on Verma modules

Dan Barbasch (1983)

Annales scientifiques de l'École Normale Supérieure

Finite dimensional modules of some quantum groups over Fp (v).

Xi Nanhua (1990)

Journal für die reine und angewandte Mathematik

Free associative algebras, noncommutative Gröbner bases, and universal associative envelopes for nonassociative structures

Murray R. Bremner (2014)

Commentationes Mathematicae Universitatis Carolinae

First, we provide an introduction to the theory and algorithms for noncommutative Gröbner bases for ideals in free associative algebras. Second, we explain how to construct universal associative envelopes for nonassociative structures defined by multilinear operations. Third, we extend the work of Elgendy (2012) for nonassociative structures on the 2-dimensional simple associative triple system to the 4- and 6-dimensional systems.

Gelfand-Kirillov Dimension for Harish-Chandra Modules.

David A., Jr. Vogan (1978)

Inventiones mathematicae

Générateurs de l’algèbre $𝒰 {(G)}^{K}$ avec $G = S O (m)$ ou $S O_{0} (1, m - 1)$ et $K = S O (m - 1)$

Abdel-Ilah Benabdallah (1983)

Bulletin de la Société Mathématique de France

Générateurs de l’algèbre $𝒰 {(G)}^{K}$ avec $G = S O (m)$ ou $S O_{o} (1, m - 1)$ et $K = S O (m - 1)$

Abdel-Ilah Benabdallah (1982)

Publications du Département de mathématiques (Lyon)

Generators and relations for Schur algebras.

Doty, Stephen, Giaquinto, Anthony (2001)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Generators for the divided powers algebra of an algebra and trace identities

Dieter Ziplies (1987)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Groupes quantiques

Jean-Louis Verdier (1986/1987)

Séminaire Bourbaki

Hall algebras and quantum groups.

Claus Michael Ringel (1990)

Inventiones mathematicae

Hochschild homology and cohomology of generalized Weyl algebras

Marco A. Farinati, Andrea L. Solotar, Mariano Suárez-Álvarez (2003)

Annales de l’institut Fourier

We compute Hochschild homology and cohomology of a class of generalized Weyl algebras, introduced by V. V. Bavula in St. Petersbourg Math. Journal, 4 (1) (1999), 71-90. Examples of such algebras are the n-th Weyl algebras, $𝒰 (𝔰 𝔩_{2})$ , primitive quotients of $𝒰 (𝔰 𝔩_{2})$ , and subalgebras of invariants of these algebras under finite cyclic groups of automorphisms. We answer a question of Bavula–Jordan (Trans. A.M.S., 353 (2) (2001), 769-794) concerning the generators of the group of automorphisms of a generalized Weyl...

Currently displaying 41 – 60 of 182

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Displaying 41 – 60 of 182

Enveloping algebras of Slodowy slices and the Joseph ideal

Equivariant deformation quantization for the cotangent bundle of a flag manifold

Euclidean components for a class of self-injective algebras

Exact Borel subalgebras of quasi-heriditary algebras, I (with an appendix by Leonard Scott).

Fair-sized projective modules

Family algebras.

Filtrations on Verma modules

Finite dimensional modules of some quantum groups over Fp (v).

Free associative algebras, noncommutative Gröbner bases, and universal associative envelopes for nonassociative structures

Gelfand-Kirillov Dimension for Harish-Chandra Modules.

Générateurs de l’algèbre $𝒰 {(G)}^{K}$ avec $G = S O (m)$ ou $S O_{0} (1, m - 1)$ et $K = S O (m - 1)$

Générateurs de l’algèbre $𝒰 {(G)}^{K}$ avec $G = S O (m)$ ou $S O_{o} (1, m - 1)$ et $K = S O (m - 1)$

Generators and relations for Schur algebras.

Generators for the divided powers algebra of an algebra and trace identities

Groupes quantiques

Hall algebras and quantum groups.

Hochschild homology and cohomology of generalized Weyl algebras

Homologie de quotients primitifs de l'algèbre enveloppante de ...l(2).

Homomorphisms of semiholonomic Verma modules: An exceptional case.

Idéaux à gauche dans les quotients simples de l’algèbre enveloppante de $s l (2)$

Currently displaying 41 – 60 of 182