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

Given a field $k$ of characteristic zero, let R = k_-1[x₁, ..., x_n] denote the $(-1)$ skew-polynomial ring; i.e., the ring generated from $n$ indeterminates \{x_i\}_i=1ⁿ 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.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2017

Author dc:creator

• Hall, Bailey Thomas

• Algebra Generator

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/82199

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/82199