Article
| Title: | Tensor products of higher almost split sequences in subcategories (English) |
| Author: | Lu, Xiaojian |
| Author: | Luo, Deren |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 1151-1174 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We introduce the algebras satisfying the $(\mathcal B,n)$ condition. If $\Lambda $, $\Gamma $ are algebras satisfying the $(\mathcal B,n)$, $(\mathcal E,m)$ condition, respectively, we give a construction of $(m+n)$-almost split sequences in some subcategories $(\mathcal B\otimes \mathcal E)^{(i_0, j_0)}$ of $\mod (\Lambda \otimes \Gamma )$ by tensor products and mapping cones. Moreover, we prove that the tensor product algebra $\Lambda \otimes \Gamma $ satisfies the $((\mathcal B\otimes \mathcal E)^{(i_0, j_0)},n+m)$ condition for some integers $i_0$, $j_0$; this construction unifies and extends the work of A. Pasquali (2017), (2019). (English) |
| Keyword: | $n$-representation finite algebra |
| Keyword: | higher almost split sequence |
| Keyword: | tensor product |
| Keyword: | mapping cone |
| MSC: | 16D90 |
| MSC: | 16G10 |
| MSC: | 16G70 |
| DOI: | 10.21136/CMJ.2023.0432-22 |
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| Date available: | 2023-11-23T12:24:10Z |
| Last updated: | 2023-11-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151952 |
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