Enveloping Algebras and Cohomology of Leibniz Pairs

Published 9 Apr 2013 in math.RT | (1304.2636v1)

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.

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