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n-ary Lie and Associative Algebras

Peter W. Michor·Alexandre M. Vinogradov
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Abstract

With the help of the multigraded Nijenhuis-- Richardson bracket and the multigraded Gerstenhaber bracket from [7] for every $n\ge 2$ we define $n$-ary associative algebras and their modules and also $n$-ary Lie algebras and their modules, and we give the relevant formulas for Hochschild and Chevalley cohomogy.

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Peter W. Michor, Alexandre M. Vinogradov. 1998-01-19. n-ary Lie and Associative Algebras. https://arxiv.org/abs/math/9801087

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