<var/>N</var>-homogeneous superalgebras

Abstract

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”.