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Dual Reflection Groups of Low Order

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abstract
We consider group-gradings of noncommutative algebras with the following question in mind: for what groups $G$ does there exist an Artin-Schelter regular algebra $A$ with $G$ grading $A$ such that $A_e$, the identity-graded component of $A$, is itself Artin-Schelter regular? And in particular, restricting further, what if we require $A$ to be a quadratic domain? Results exist regarding the Poincar\'e polynomial of a group with respect to an arbitrary generating set that grades an Artin-Schelter regular algebra in this way, which we use to narrow down possible grades of the generators of $A$.
subject
Algebra
Invariant Theory
Noncommutative Algebra
contributor
Vashaw, Kent Barton (author)
Kirkman, Ellen (committee chair)
Rouse, Jeremy (committee member)
Moore, Frank (committee member)
date
2016-05-21T08:35:52Z (accessioned)
2016-05-21T08:35:52Z (available)
2016 (issued)
degree
Mathematics (discipline)
identifier
http://hdl.handle.net/10339/59320 (uri)
language
en (iso)
publisher
Wake Forest University
title
Dual Reflection Groups of Low Order
type
Thesis

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