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Communications in Algebra Volume 43, 2015 - Issue 10
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Original Articles

Enveloping Algebras and Cohomology of Leibniz Pairs

Yan-Hong Bao School of Mathematical Sciences, Anhui University, Hefei, Anhui, China; School of Mathematical Sciences, University of Sciences and Technology in China, Hefei, Anhui, ChinaCorrespondence[email protected]
&
Yu Ye School of Mathematical Sciences, University of Sciences and Technology in China, Hefei, Anhui, China; Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei, China
Pages 4487-4501 | Received 24 May 2013, Published online: 06 Jul 2015
 
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Abstract

We introduce the enveloping algebra for a Leibniz pair, and show that the category of modules over a Leibniz pair is isomorphic to the category of left modules over its enveloping algebra. Consequently, we show that the cohomology theory for a Leibniz pair introduced by Flato, Gerstenhaber, and Voronov can be interpreted by Ext-groups of modules over the enveloping algebra.

2010 Mathematics Subject Classification:

Notes

Communicated by J. Alev.

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