On Reflection Representations of Coxeter Groups over Non-Commutative Rings

Annette Pilkingtonn

Published 2021-07-04Version 1

In this paper, we consider representations of Coxeter groups over a path algebra, R, defined by Dyer. We answer a question posed by Dyer about the multiplicative properties of R, showing that it is "almost a domain". We also show that R cam be embedded in a matrix ring over a free product of extension fields of the rational numbers and rings of Laurent polynomials.