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N-homogeneous superalgebras

Benoit Kriegk, Martin Lorenz, Phùng Hô Hai

Number 7
Author Phùng Hô Hai
Year 2007

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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