Invariants of (-1)-Skew Polynomial Rings under Permutation Representations
Rings and Algebras
2013-05-20 v1
Abstract
The symmetric group S_n acts on the skew polynomial ring A=k_{-1}[x_1,..., x_n] as permutations. For subgroups G of S_n we consider properties of the ring of invariants A^G. We show that A^G is always Artin-Schelter Gorenstein, and we investigate when A^G is a "complete intersection", in a sense we define. We obtain bounds on the degrees of the algebra generators. The properties of A^G are compared with those in the classical case, k[x_1, ..., x_n]^G.
Keywords
Cite
@article{arxiv.1305.3973,
title = {Invariants of (-1)-Skew Polynomial Rings under Permutation Representations},
author = {Ellen E. Kirkman and James J. Kuzmanovich and James J. Zhang},
journal= {arXiv preprint arXiv:1305.3973},
year = {2013}
}
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37 pages