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Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type $A (n | 0)$ , the baby Verma modules $Z_{χ} (λ)$ are proved to be simple for any regular nilpotent $p$ -character $χ$ and typical weight $λ$ . Moreover, we obtain the dimension formulas for projective covers of simple modules with $p$ -characters of standard Levi form.

On the annihilators of the simple subquotients of the principal series

A. Joseph (1977)

Annales scientifiques de l'École Normale Supérieure

On the centralizer of K in the universal enveloping algebra of SO(n,1) and SU(n,1).

Juan A. Tirao (1994)

Manuscripta mathematica

On the Characterization of Primitive Ideals in Enveloping Algebras.

Ronald S. Irving, Lance W. Small (1980)

Mathematische Zeitschrift

On the classification of primitive ideals for complex classical Lie algebras, II

Devra Garfinkle (1992)

Compositio Mathematica

On the classification of primitive ideals for complex classical Lie algebras, I

Devra Garfinkle (1990)

Compositio Mathematica

On the classification of primitive ideals for complex classical Lie algebras, III

Devra Garfinkle (1993)

Compositio Mathematica

On the double Poincaré series of the enveloping algebras of certain graded Lie algebras.

Calle Jacobsson (1982)

Mathematica Scandinavica

On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case

Anthony Joseph (1979)

Bulletin de la Société Mathématique de France

On the ghost centre of Lie superalgebras

Maria Gorelik (2000)

Annales de l'institut Fourier

We study the invariants of the universal enveloping algebra of a Lie superalgebra with respect to a certain “twisted” adjoint action.

On the Hattori-Stallings trace for certain primitive factors of enveloping algebras of semisimple Lie algebras.

Gadi S. Perets, Patrick Polo (1995)

Mathematische Zeitschrift

On the homology of free Lie algebras

Calin Popescu (1998)

Commentationes Mathematicae Universitatis Carolinae

Given a principal ideal domain $R$ of characteristic zero, containing $1 / 2$ , and a connected differential non-negatively graded free finite type $R$ -module $V$ , we prove that the natural arrow $𝕃 F H (V) \to F H 𝕃 (V)$ is an isomorphism of graded Lie algebras over $R$ , and deduce thereby that the natural arrow $U F H 𝕃 (V) \to F H U 𝕃 (V)$ is an isomorphism of graded cocommutative Hopf algebras over $R$ ; as usual, $F$ stands for free part, $H$ for homology, $𝕃$ for free Lie algebra, and $U$ for universal enveloping algebra. Related facts and examples are also considered....

On the infinitesimal kernel of irreducible representations of nilpotent Lie groups

Niels Vigand Pedersen (1984)

Bulletin de la Société Mathématique de France

On the Joseph-small additivity principle for goldie ranks. A study on extensions of noetherian rings with applications to enveloping algebras

Walter Borho (1982)

Compositio Mathematica

On the $K$ -theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case

Patrick Polo (1995)

Annales de l'institut Fourier

Let $G$ be a semisimple complex algebraic group and $X$ its flag variety. Let $𝔤 = Lie (G)$ and let $U$ be its enveloping algebra. Let $𝔥$ be a Cartan subalgebra of $𝔤$ . For $μ \in 𝔥^{*}$ , let $J_{μ}$ be the corresponding minimal primitive ideal, let $U_{μ} = U / J_{μ}$ , and let $𝒯_{U_{μ}} : K_{0} (U_{m} u) \to ℂ$ be the Hattori-Stallings trace. Results of Hodges suggest to study this map as a step towards a classification, up to isomorphism or Morita equivalence, of the $ℂ$ -algebras $U_{μ}$ . When $μ$ is regular, Hodges has shown that $K_{0} (U_{μ}) ≅ K_{0} (X)$ . In this case $K_{0} (U_{μ})$ is generated by the classes corresponding to...

On universal enveloping algebras in a topological setting

Daniel Beltiţă, Mihai Nicolae (2015)

Studia Mathematica

We study some embeddings of suitably topologized spaces of vector-valued smooth functions on topological groups, where smoothness is defined via differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensional Lie groups...

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