Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Reflection Representations of Coxeter Groups over Non-Commutative
  Rings   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.

27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th