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

2013/05/17 by Ellen E. Kirkman, Kirkman, Ellen E., James J. Kuzmanovich +3
Mathematics · #16A62 #16E70 #20J50 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16A62 #msc:16E70 #msc:20J50

paper · pdf · doi:10.48550/arxiv.1305.3973

37 pages

arxiv created 2013/05/17 · arxiv updated 2013/05/20

Abstract

The symmetric group S_n acts on the skew polynomial ring A=k_-1[x₁,..., 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[x₁, ..., x_n]^G.

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