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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.02537 |
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| _version_ | 1866910002622496768 |
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| author | Liu, Yuming Xing, Bohan |
| author_facet | Liu, Yuming Xing, Bohan |
| contents | By providing equivalent definitions of fractional Brauer configuration algebras in certain special cases, we associate to each monomial algebra some combinatorial data called a fractional Brauer configuration, from which we construct a corresponding fractional Brauer configuration algebra. We show that this algebra is isomorphic to the trivial extension of the given monomial algebra. Furthermore, we establish a one-to-one correspondence between the isomorphism classes of monomial algebras and the equivalence classes of pairs consisting of a symmetric fractional Brauer configuration algebra of type S with a free fractional-degree function and an admissible cut on it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras Liu, Yuming Xing, Bohan Rings and Algebras 16G20, 16G10, 16S99 By providing equivalent definitions of fractional Brauer configuration algebras in certain special cases, we associate to each monomial algebra some combinatorial data called a fractional Brauer configuration, from which we construct a corresponding fractional Brauer configuration algebra. We show that this algebra is isomorphic to the trivial extension of the given monomial algebra. Furthermore, we establish a one-to-one correspondence between the isomorphism classes of monomial algebras and the equivalence classes of pairs consisting of a symmetric fractional Brauer configuration algebra of type S with a free fractional-degree function and an admissible cut on it. |
| title | Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras |
| topic | Rings and Algebras 16G20, 16G10, 16S99 |
| url | https://arxiv.org/abs/2408.02537 |