N-homogeneous superalgebras
Quantum Algebra
2007-06-13 v2 Combinatorics
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 -generalized super-version of MacMahon's classical "master theorem".
Cite
@article{arxiv.0704.1888,
title = {N-homogeneous superalgebras},
author = {Phung Ho Hai and Benoit Kriegk and Martin Lorenz},
journal= {arXiv preprint arXiv:0704.1888},
year = {2007}
}
Comments
42 pages, LaTeX; typos corrected, several references added, introduction slightly expanded