Nonlinear maps satisfying derivability on the parabolic subalgebras of the general linear Lie algebras

2012 ◽  
Vol 60 (2) ◽  
pp. 149-157 ◽  
Author(s):  
Zhengxin Chen ◽  
Dengyin Wang
Keyword(s):  
Lie Algebras ◽  
General Linear ◽  
Parabolic Subalgebras ◽  
Nonlinear Maps

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.

Affine Lie Algebra Modules and Complete Lie Algebras

2006 ◽  
Vol 13 (03) ◽  
pp. 481-486
Author(s):  
Yongcun Gao ◽  
Daoji Meng
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Infinite Dimensional ◽  
Affine Lie Algebra ◽  
Parabolic Subalgebras ◽  
Integrable Modules

In this paper, we first construct some new infinite dimensional Lie algebras by using the integrable modules of affine Lie algebras. Then we prove that these new Lie algebras are complete. We also prove that the generalized Borel subalgebras and the generalized parabolic subalgebras of these Lie algebras are complete.

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