Article
| Title: | Hall algebra of morphism category (English) |
| Author: | Chen, QingHua |
| Author: | Zhang, Liwang |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 4 |
| Year: | 2024 |
| Pages: | 1145-1164 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | This paper investigates a universal PBW-basis and a minimal set of generators for the Hall algebra $\mathcal {H}(C_2(\mathcal {P}))$, where $C_2(\mathcal {P})$ is the category of morphisms between projective objects in a finitary hereditary exact category $\mathcal A$. When $\mathcal A$ is the representation category of a Dynkin quiver, we develop multiplication formulas for the degenerate Hall Lie algebra $\mathcal {L}$, which is spanned by isoclasses of indecomposable objects in $C_2(\mathcal {P})$. As applications, we demonstrate that $\mathcal {L}$ contains a Lie subalgebra isomorphic to the central extension of the Heisenberg Lie algebra and construct the Borel subalgebra of the simple Lie algebra associated with $\mathcal A$ as a Lie subquotient algebra of $\mathcal {L}$. (English) |
| Keyword: | Hall algebra |
| Keyword: | morphism category |
| Keyword: | Heisenberg Lie algebra |
| Keyword: | simple Lie algebra |
| MSC: | 16G20 |
| MSC: | 17B20 |
| MSC: | 17B30 |
| MSC: | 18G05 |
| DOI: | 10.21136/CMJ.2024.0103-24 |
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| Date available: | 2024-12-15T06:38:08Z |
| Last updated: | 2024-12-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152694 |
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