N-homogeneous superalgebras

Details N-homogeneous superalgebras N-homogeneous superalgebras

2007-04-14

arxiv.org/abs/0704.1888v2

Mathematics

Quantum Algebra

42 pages, LaTeX; typos corrected, several references added, introduction slightly expanded

Scientific paper

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

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