Cohomologies and generalized derivation extensions of n-Lie algebras

2021/04/18 by Ateşli, B., Esen, O., Sütlü, S.
#17A32 #17A36 #17A40 #17A42 #17B56 #18G40 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2104.08871

Abstract

A cohomology theory, associated to a n-Lie algebra and a representation space of it, is introduced. It is observed that this cohomology theory is qualified to encode the generalized derivation extensions, and that it coincides, for n=3, with the known cohomology of n-Lie algebras. The abelian extensions and infinitesimal deformations of n-Lie algebras, on the other hand, are shown to be characterized by the usual cohomology of n-Lie algebras. Furthermore, the Hochschild-Serre spectral sequence of the Lie algebra cohomology is upgraded to the level of n-Lie algebras, and is applied to the cohomology of generalized derivation extensions.

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