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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A cohomological characterization of Leibniz central extensions of Lie algebras


Authors: Naihong Hu, Yufeng Pei and Dong Liu
Journal: Proc. Amer. Math. Soc. 136 (2008), 437-447
MSC (2000): Primary 17A32, 17B56; Secondary 17B65
Published electronically: October 24, 2007
MathSciNet review: 2358481
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Abstract | References | Similar Articles | Additional Information

Abstract: Mainly motivated by Pirashvili's spectral sequences on a Leibniz algebra, a cohomological characterization of Leibniz central extensions of Lie algebras is given. In particular, as applications, we obtain the cohomological version of Gao's main theorem for Kac-Moody algebras and answer a question in an earlier paper by Liu and Hu (2004).


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Additional Information

Naihong Hu
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China
Email: nhhu@euler.math.ecnu.edu.cn

Yufeng Pei
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China
Email: peiyufeng@gmail.com

Dong Liu
Affiliation: Department of Mathematics, Huzhou Teachers College, Zhejiang, Huzhou 313000, People’s Republic of China
Email: liudong@hytc.zj.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08985-X
PII: S 0002-9939(07)08985-X
Keywords: Leibniz central extensions, Leibniz cohomology, invariant symmetric bilinear forms, dual space derivations.
Received by editor(s): May 17, 2006
Received by editor(s) in revised form: October 28, 2006
Published electronically: October 24, 2007
Additional Notes: This work is supported in part by the NNSF (Grants 10431040, 10671027, 10701019), the TRAPOYT and the FUDP from the MOE of China, and the SRSTP from the STCSM
Communicated by: Dan M. Barbasch
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.