ALGEBRA GENERATORS AND HILBERT SERIES OF Z(K_{-1}[X_1, ..., X_n]^{S_n})
type: CreativeWork
description: 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.
abstract: 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.
author: Hall, Bailey Thomas
language: en
keywords: Algebra Generator
date published: 2017
date modified: 2026-07-27T22:02:11Z
provider: Wake Forest University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Wake Forest University

PropertyValue
property ID: Handle
value: http://hdl.handle.net/10339/82199