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arXiv · 2107.01530

On Reflection Representations of Coxeter Groups over Non-Commutative Rings

Annette Pilkingtonn
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Abstract

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.

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BibTeXRIS

Annette Pilkingtonn. 2021-07-04. On Reflection Representations of Coxeter Groups over Non-Commutative Rings. https://arxiv.org/abs/2107.01530

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