Journal of Noncommutative Geometry

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Volume 2, Issue 1, 2008, pp. 1–51
DOI: 10.4171/JNCG/15

N-homogeneous superalgebras

Phùng Hô Hai[1], Benoît Kriegk[2] and Martin Lorenz[3]

(1) Fachbereich Mathematik, Campus Essen, Universität Duisburg-Essen, 45117, ESSEN, GERMANY
(2) Laboratoire de Mathématiques, Université Jean-Monnet, 23, rue du Docteur Paul Michelon, 42023, SAINT-ETIENNE CEDEX 2, FRANCE
(3) Department of Mathematics, Temple University, PA 19122-6094, PHILADELPHIA, UNITED STATES

We develop the theory of N-homogeneous algebras in a super-setting, with particular emphasis on the Koszul property. To any Hecke operator ℛ on a vector superspace, we associate certain superalgebras Sℛ,N and Λℛ,N generalizing the ordinary symmetric and Grassmann algebra, respectively. We prove that these algebras are N-Koszul. For the special case where ℛ is the ordinary supersymmetry, we derive an N-generalized super-version of MacMahon’s classical “master theorem”.

Keywords: Superalgebra, generalized Koszul algebra, N-homogeneous algebra, Hecke algebra, MacMahon's master theorem, binomial identity, Berezinian

Hai Phùng Hô, Kriegk Benoît, Lorenz Martin: N-homogeneous superalgebras. J. Noncommut. Geom. 2 (2008), 1-51. doi: 10.4171/JNCG/15