n-ary Lie and Associative Algebras

1998/01/19 by Peter W. Michor, Alexandre M. Vinogradov · 1 citation
Mathematics · #math.QA #msc:08A62 #msc:16B99 #msc:17B99

paper · pdf

published as Rend. Sem. Mat. Univ. Pol. Torino, 53, 4 (1996), 373-392 · 18 pages, AmSTeX

arxiv created 1998/01/19 · arxiv updated 2009/11/30

Abstract

With the help of the multigraded Nijenhuis-- Richardson bracket and the multigraded Gerstenhaber bracket from [7] for every n≥ 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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