Trivial central extensions of Lie bialgebras

JOURNAL OF ALGEBRA

卷:390

Article

Farinati, Marco A.¹  Jancsa, Alejandra Patricia¹ 

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dto Matemat, RA-1428 Buenos Aires, DF, Argentina

关键词: Lie bialgebras;    Extensions;    Derivations;   

DOI  :  10.1016/j.jalgebra.2013.05.011

来源: Elsevier

【 摘 要 】

From a Lie algebra g satisfying Z(g) = 0 and Lambda(2)(g)(g) = 0 (in particular, for g semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form Sigma = g x K in terms of Lie bialgebra structures on g (not necessarily factorizable nor quasi-triangular) and its biderivations, for any field IK of characteristic different form 2, 3. If moreover, [g, g] = g, then we describe also all Lie bialgebra structures on extensions Sigma = g x K-n. In interesting cases we characterize the Lie algebra of biderivations. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free