N-homogeneous superalgebras
(with Phung Ho Hai and Benoit Kriegk)

 

Publication status: appeared in
Journal of Noncommutative Geometry 2, 1-51 (2008); arXiv: http://arxiv.org/abs/0704.1888 
 
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 generalizing the ordinary
symmetric and the Grassmann algebra. 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" involving the Berezinian.


 

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