Braided m-Lie Algebras |
| |
Authors: | Shouchuan Zhang Yao-Zhong Zhang |
| |
Institution: | (1) Department of Mathematics, Hunan University, Changsha, P.R. China, 410082;(2) Department of Mathematics, University of Queensland, Brisbane, 4072, Australia |
| |
Abstract: | Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of End
F
M, where M is a Yetter–Drinfeld module over B with dimB < . In particular, generalized classical braided m-Lie algebras sl
q, f
(GM
G
(A), F) and osp
q, t
(GM
G
(A), M, F) of generalized matrix algebra GM
G
(A) are constructed and their connection with special generalized matrix Lie superalgebra sl
s, f
(GM
Z_2(A
s
), F) and orthosymplectic generalized matrix Lie super algebra osp
s, t
(GM
Z_2(A
s
), M
s
, F) are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established.This revised version was published online in March 2005 with corrections to the cover date. |
| |
Keywords: | lie algebras braided algebras quantum algebras |
本文献已被 SpringerLink 等数据库收录! |
|