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ISRN Algebra
Volume 2011 (2011), Article ID 381875, 11 pages
http://dx.doi.org/10.5402/2011/381875
Research Article

𝑇 βˆ— πœƒ -Extensions of 𝑛 -Lie Algebras

College of Mathematics and Computer Science, Hebei University, Baoding 071002, China

Received 28 May 2011; Accepted 6 July 2011

Academic Editors: W. de Graaf and A. Zimmermann

Copyright Β© 2011 Ruipu Bai and Ying Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper is mainly concerned with 𝑇 βˆ— πœƒ -extensions of 𝑛 -Lie algebras. The 𝑇 βˆ— πœƒ -extension 𝐿 πœƒ ( 𝐿 βˆ— ) of an 𝑛 -Lie algebra 𝐿 by a cocycle θ is defined, and a class of cocycles is constructed by means of linear mappings from an 𝑛 -Lie algebra on to its dual space. Finally all 𝑇 βˆ— πœƒ -extensions of ( 𝑛 + 1 ) -dimensional 𝑛 -Lie algebras are classified, and the explicit multiplications are given.