2026-09-22T07:49:46Zhttps://wakespace.lib.wfu.edu/server/oai/request

oai:null:10339/821992026-09-02T10:54:02Zcom_10339_14934col_10339_38132

Hall, Bailey Thomas 2017-06-15T08:35:57Z 2017-06-15T08:35:57Z 2017 https://wakespace.lib.wfu.edu/handle/10339/82199 Given a field $k$ of characteristic zero, let $R = k_{-1}[x_1, ..., x_n]$ denote the $(-1)$ skew-polynomial ring; i.e., the ring generated from $n$ indeterminates $\{x_i\}_{i=1}^n$ over $k$ such that $x_i x_j = - x_j x_i$ for all $i \ne j$. If $G$ is a subgroup of the symmetric group $S_n$ represented by permutation matrices, there is an induced $G$-action on $R$ given by permuting the indeterminates. We define $R^G$ as the subring of invariants under this $G$-action. In this thesis, we determine the algebra generators and the Hilbert series of the center of $R^{S_n}$, denoted $Z(R^{S_n})$. Moreover, we determine an algorithm for determining the ideal of relations on the generators. en Wake Forest University Algebra Generator Center Hilbert Series Invariant Ring Orbit Sum Skew-Polynomial ALGEBRA GENERATORS AND HILBERT SERIES OF Z(K_{-1}[X_1, ..., X_n]^{S_n}) Thesis Moore, William F Kirkman, Ellen E Rouse, Jeremy Mathematics and Statistics open.access