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arXiv · 1305.3973

Invariants of (-1)-Skew Polynomial Rings under Permutation Representations

Ellen E. Kirkman·James J. Kuzmanovich·James J. Zhang
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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.

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Ellen E. Kirkman, James J. Kuzmanovich, James J. Zhang. 2013-05-17. Invariants of (-1)-Skew Polynomial Rings under Permutation Representations. https://arxiv.org/abs/1305.3973

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