Subregular J-Rings of the Finite Irreducible Coxeter Systems
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866917122592997376 |
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| author | Pilkington, Annette |
| author_facet | Pilkington, Annette |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_11425 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Subregular J-Rings of the Finite Irreducible Coxeter Systems Pilkington, Annette Rings and Algebras 20F55, 16S88 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. |
| title | Subregular J-Rings of the Finite Irreducible Coxeter Systems |
| topic | Rings and Algebras 20F55, 16S88 |
| url | https://arxiv.org/abs/2107.11425 |