Blocks and projective modules for reduced universal enveloping algebras of a nilpotent restricted Lie algebra

1995 ◽  
Vol 65 (6) ◽  
pp. 495-500 ◽  
Author(s):  
J�rg Feldvoss
Keyword(s):  
Lie Algebra ◽  
Projective Modules ◽  
Universal Enveloping Algebras ◽  
Enveloping Algebras ◽  
Restricted Lie Algebra

scholarly journals TWO PERMANENTS IN THE UNIVERSAL ENVELOPING ALGEBRAS OF THE SYMPLECTIC LIE ALGEBRAS

2009 ◽  
Vol 20 (03) ◽  
pp. 339-368 ◽  
Author(s):  
MINORU ITOH
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Universal Enveloping Algebra ◽  
Irreducible Representations ◽  
General Linear ◽  
Universal Enveloping Algebras ◽  
Enveloping Algebras ◽  
Enveloping Algebra ◽  
Central Elements ◽  
Orthogonal Lie Algebra

This paper presents new generators for the center of the universal enveloping algebra of the symplectic Lie algebra. These generators are expressed in terms of the column-permanent and it is easy to calculate their eigenvalues on irreducible representations. We can regard these generators as the counterpart of central elements of the universal enveloping algebra of the orthogonal Lie algebra given in terms of the column-determinant by Wachi. The earliest prototype of all these central elements is the Capelli determinants in the universal enveloping algebra of the general linear Lie algebra.

Some Norms on Universal Enveloping Algebras

1998 ◽  
Vol 50 (2) ◽  
pp. 356-377 ◽  
Author(s):  
Leonard Gross
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Dual Space ◽  
Universal Enveloping Algebras ◽  
Enveloping Algebras ◽  
Enveloping Algebra ◽  
Kernel Analysis ◽  
Finite Rank Elements ◽  
Heat Kernel Analysis ◽  
Algebra Level

AbstractThe universal enveloping algebra, U(𝔤), of a Lie algebra 𝔤 supports some norms and seminorms that have arisen naturally in the context of heat kernel analysis on Lie groups. These norms and seminorms are investigated here from an algebraic viewpoint. It is shown that the norms corresponding to heat kernels on the associated Lie groups decompose as product norms under the natural isomorphism . The seminorms corresponding to Green's functions are examined at a purely Lie algebra level for sl (2, ℂ). It is also shown that the algebraic dual space U′ is spanned by its finite rank elements if and only if 𝔤 is nilpotent.

scholarly journals Vector bundles associated to Lie algebras

2016 ◽  
Vol 2016 (716) ◽  
Author(s):  
Jon F. Carlson ◽  
Eric M. Friedlander ◽  
Julia Pevtsova
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Vector Bundles ◽  
Coherent Sheaves ◽  
Restricted Lie Algebra ◽  
Finite Dimensional

AbstractWe introduce and investigate a functorial construction which associates coherent sheaves to finite dimensional (restricted) representations of a restricted Lie algebra

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