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ALGEBRA GENERATORS AND HILBERT SERIES OF Z(K_{-1}[X_1, ..., X_n]^{S_n})

Electronic Theses and Dissertations

Item Details

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.
subject
Algebra Generator
Center
Hilbert Series
Invariant Ring
Orbit Sum
Skew-Polynomial
contributor
Moore, William F (committee chair)
Kirkman, Ellen E (committee member)
Rouse, Jeremy (committee member)
date
2017-06-15T08:35:57Z (accessioned)
2017-06-15T08:35:57Z (available)
2017 (issued)
degree
Mathematics and Statistics (discipline)
identifier
http://hdl.handle.net/10339/82199 (uri)
language
en (iso)
publisher
Wake Forest University
title
ALGEBRA GENERATORS AND HILBERT SERIES OF Z(K_{-1}[X_1, ..., X_n]^{S_n})
type
Thesis