n-ary Lie and Associative Algebras

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.

18 pages, AmSTeX

References in corpus (3)

• New Generalized Poisson Structures
• Knit products of graded Lie algebras and groups
• The multigraded Nijenhuis-Richardson Algebra, its universal property and application

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• Semiheaps and Ternary Algebras in Quantum Mechanics Revisited
• Ternary numbers and algebras. Reflexive numbers and Berger graphs
• Arity shape of polyadic algebraic structures
• On Filippov algebroids and multiplicative Nambu-Poisson structures
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• On the associative homotopy Lie algebras and the Wronskians
• Hyperpolyadic structures
• Polyadic systems, representations and quantum groups
• On the $n$-ary algebras, semigroups and their universal covers
• Membership deformation of commutativity and obscure $n$-ary algebras
• Commutative $n$-ary superalgebras with an invariant skew-symmetric form