The Green ring of a restricted enveloping algebra in characteristic 2
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908659465846784 |
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| author | Andruskiewitsch, Nicolás Bagio, Dirceu Della Flora, Saradia Flôres, Daiana |
| author_facet | Andruskiewitsch, Nicolás Bagio, Dirceu Della Flora, Saradia Flôres, Daiana |
| contents | Let $\Bbbk$ be an algebraically closed field of characteristic $2$ and let $\mathfrak{fsl}(2)$ be the unique, up to isomorphism, $3$-dimensional simple Lie algebra over $\Bbbk$. Denote by $\mathfrak{m}$ the minimal $2$-envelope of $\mathfrak{fsl}(2)$ and by $\mathfrak{u}(\mathfrak{m})$ its corresponding restricted enveloping algebra. The non-isomorphic finite-dimensional indecomposable $\mathfrak{u}(\mathfrak{m})$-modules were classified in \cite{ABDF}. In this paper, the Green ring (or representation ring) for $\mathfrak{u}(\mathfrak{m})$ is calculated. Also, the semisimplification of the representation category of $\mathfrak{u}(\mathfrak{m})$ is determined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13345 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Green ring of a restricted enveloping algebra in characteristic 2 Andruskiewitsch, Nicolás Bagio, Dirceu Della Flora, Saradia Flôres, Daiana Representation Theory Quantum Algebra Let $\Bbbk$ be an algebraically closed field of characteristic $2$ and let $\mathfrak{fsl}(2)$ be the unique, up to isomorphism, $3$-dimensional simple Lie algebra over $\Bbbk$. Denote by $\mathfrak{m}$ the minimal $2$-envelope of $\mathfrak{fsl}(2)$ and by $\mathfrak{u}(\mathfrak{m})$ its corresponding restricted enveloping algebra. The non-isomorphic finite-dimensional indecomposable $\mathfrak{u}(\mathfrak{m})$-modules were classified in \cite{ABDF}. In this paper, the Green ring (or representation ring) for $\mathfrak{u}(\mathfrak{m})$ is calculated. Also, the semisimplification of the representation category of $\mathfrak{u}(\mathfrak{m})$ is determined. |
| title | The Green ring of a restricted enveloping algebra in characteristic 2 |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2511.13345 |