Title: | Hall algebras of two equivalent extriangulated categories (English) |
Author: | Ruan, Shiquan |
Author: | Wang, Li |
Author: | Zhang, Haicheng |
Language: | English |
Journal: | Czechoslovak Mathematical Journal |
ISSN: | 0011-4642 (print) |
ISSN: | 1572-9141 (online) |
Volume: | 74 |
Issue: | 1 |
Year: | 2024 |
Pages: | 95-113 |
Summary lang: | English |
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Category: | math |
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Summary: | For any positive integer $n$, let $A_n$ be a linearly oriented quiver of type $A$ with $n$ vertices. It is well-known that the quotient of an exact category by projective-injectives is an extriangulated category. We show that there exists an extriangulated equivalence between the extriangulated categories $\mathcal {M}_{n+1}$ and $\mathcal {F}_n$, where $\mathcal {M}_{n+1}$ and $\mathcal {F}_n$ are the two extriangulated categories corresponding to the representation category of $A_{n+1}$ and the morphism category of projective representations of $A_n$, respectively. As a by-product, the Hall algebras of $\mathcal {M}_{n+1}$ and $\mathcal {F}_n$ are isomorphic. As an application, we use the Hall algebra of $\mathcal {M}_{2n+1}$ to relate with the quantum cluster algebras of type $A_{2n}$. (English) |
Keyword: | extriangulated category |
Keyword: | extriangulated equivalence |
Keyword: | Hall algebra |
Keyword: | quantum cluster algebra |
MSC: | 17B37 |
MSC: | 18E05 |
MSC: | 18E10 |
DOI: | 10.21136/CMJ.2023.0344-22 |
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Date available: | 2024-03-13T10:04:43Z |
Last updated: | 2024-03-18 |
Stable URL: | http://hdl.handle.net/10338.dmlcz/152270 |
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