2007/04/14 by Hai, Phung Ho, Kriegk, Benoit, Lorenz, Martin · 1 citation
#05A19 #16S37 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.0704.1888
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".