A Characteristic free approach to skew-gentle algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913186189410304 |
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| author | Chen, Yiping |
| author_facet | Chen, Yiping |
| contents | To each skew-gentle algebra, one can assign a gentle algebra in terms of combinatorial data. In order to relate the structures of the two algebras, we establish a homological epimorphism and a recollement of derived module categories. This approach is characteristic free and works in particular also in characteristic two, which is the difficult case for skew-gentle algebras. This allows to solve open problems and to uniformly reprove and strengthen known results, for instance, (1) a complete classification of selfinjective skew-gentle algebras; (2) the finitistic dimension conjecture, Auslander and Reiten's conjecture, and Keller's conjecture hold for all skew-gentle algebras; (3) a precise connection of K-theory between skew-gentle algebras and gentle algebras; (4) all skew-gentle algebras are Gorenstein, and skew-gentle algebras and their gentle algebras share the same singularity categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06467 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Characteristic free approach to skew-gentle algebras Chen, Yiping Representation Theory To each skew-gentle algebra, one can assign a gentle algebra in terms of combinatorial data. In order to relate the structures of the two algebras, we establish a homological epimorphism and a recollement of derived module categories. This approach is characteristic free and works in particular also in characteristic two, which is the difficult case for skew-gentle algebras. This allows to solve open problems and to uniformly reprove and strengthen known results, for instance, (1) a complete classification of selfinjective skew-gentle algebras; (2) the finitistic dimension conjecture, Auslander and Reiten's conjecture, and Keller's conjecture hold for all skew-gentle algebras; (3) a precise connection of K-theory between skew-gentle algebras and gentle algebras; (4) all skew-gentle algebras are Gorenstein, and skew-gentle algebras and their gentle algebras share the same singularity categories. |
| title | A Characteristic free approach to skew-gentle algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2212.06467 |