Generalized Bessel series and multiplicity problem in complex semisimple Lie algebra theory

1981 ◽  
Vol 22 (10) ◽  
pp. 2120-2126
Author(s):  
C. Bretin ◽  
J. P. Gazeau
Keyword(s):  
Lie Algebra ◽  
Semisimple Lie Algebra ◽  
Complex Semisimple ◽  
Algebra Theory

scholarly journals Separation of Variables for

2005 ◽  
Vol 48 (4) ◽  
pp. 587-600 ◽  
Author(s):  
Samuel A. Lopes
Keyword(s):  
Representation Theory ◽  
Lie Algebra ◽  
Analogous Result ◽  
Separation Of Variables ◽  
Positive Part ◽  
Semisimple Lie Algebra ◽  
Infinite Dimensional ◽  
Enveloping Algebra ◽  
Complex Semisimple ◽  
Quantized Enveloping Algebra

AbstractLet be the positive part of the quantized enveloping algebra . Using results of Alev–Dumas and Caldero related to the center of , we show that this algebra is free over its center. This is reminiscent of Kostant's separation of variables for the enveloping algebra U(g) of a complex semisimple Lie algebra g, and also of an analogous result of Joseph–Letzter for the quantum algebra Ŭq(g). Of greater importance to its representation theory is the fact that is free over a larger polynomial subalgebra N in n variables. Induction from N to provides infinite-dimensional modules with good properties, including a grading that is inherited by submodules.

scholarly journals KRULL DIMENSION OF AFFINOID ENVELOPING ALGEBRAS OF SEMISIMPLE LIE ALGEBRAS

2013 ◽  
Vol 55 (A) ◽  
pp. 7-26
Author(s):  
KONSTANTIN ARDAKOV ◽  
IAN GROJNOWSKI
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Krull Dimension ◽  
Semisimple Lie Algebra ◽  
Semisimple Lie Algebras ◽  
Enveloping Algebras ◽  
Enveloping Algebra ◽  
Complex Semisimple

AbstractUsing Beilinson–Bernstein localisation, we give another proof of Levasseur's theorem on the Krull dimension of the enveloping algebra of a complex semisimple Lie algebra. The proof also extends to the case of affinoid enveloping algebras.

scholarly journals Vanishing resonance and representations of Lie algebras

2015 ◽  
Vol 2015 (706) ◽  
Author(s):  
Stefan Papadima ◽  
Alexander I. Suciu
Keyword(s):  
Representation Theory ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Classical Representation ◽  
Semisimple Lie Algebra ◽  
Representations Of Lie Algebras ◽  
Complex Semisimple ◽  
Resonance Varieties

AbstractWe explore a relationship between the classical representation theory of a complex, semisimple Lie algebra 𝔤 and the resonance varieties

Exterior Powers of the Adjoint Representation

1997 ◽  
Vol 49 (1) ◽  
pp. 133-159 ◽  
Author(s):  
Mark Reeder
Keyword(s):  
Lie Algebra ◽  
Adjoint Representation ◽  
Irreducible Representations ◽  
Semisimple Lie Algebra ◽  
Complex Semisimple ◽  
Exterior Powers

AbstractExterior powers of the adjoint representation of a complex semisimple Lie algebra are decomposed into irreducible representations, to varying degrees of satisfaction.

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