n-ary Lie and Associative Algebras

Mathematics – Quantum Algebra

Scientific paper

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18 pages, AmSTeX

Scientific paper

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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