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”.
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Phùng Hô Hai, Benoît Kriegk, Martin Lorenz, <var/>N</var>-homogeneous superalgebras. J. Noncommut. Geom. 2 (2008), no. 1, pp. 1–51DOI 10.4171/JNCG/15