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arXiv · 2104.08871

Cohomologies and generalized derivation extensions of $n$-Lie algebras

B. Ateşli·O. Esen·S. Sütlü
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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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B. Ateşli, O. Esen, S. Sütlü. 2021-04-18. Cohomologies and generalized derivation extensions of $n$-Lie algebras. https://arxiv.org/abs/2104.08871

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