# 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 S_{R,N} and Λ_{R,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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