N-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 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".

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

References in corpus (4)

• Cayley-Hamilton theorem for quantum matrix algebras of GL(m|n) type
• The GL(m|n) type quantum matrix algebras II: the structure of the characteristic subalgebra and its spectral parameterization
• A generalization of Foata's fundamental transformation and its applications to the right-quantum algebra
• Non-commutative Sylvester's determinantal identity