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arXiv · 2107.11425

Subregular J-Rings of the Finite Irreducible Coxeter Systems

Annette Pilkington
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Abstract

In previous papers, the author showed that in many cases of interest there exists an isomorphism between certain path algebras related to the structure of the subregular J-rings of Coxeter systems and matrix rings over a free product of rings. For the finite irreducible Coxeter systems, the application of the isomorphism theorems was straightforward in all but a few cases. In this paper we show how the isomorphism theorems can be applied to show that the path algebras in the remaining cases are isomorphic to a direct sum of matrix rings over the rational numbers or over a direct product of field extensions of the rational numbers.

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Annette Pilkington. 2021-07-23. Subregular J-Rings of the Finite Irreducible Coxeter Systems. https://arxiv.org/abs/2107.11425

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