Mutation and torsion pairs
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866913896659419136 |
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| author | Hügel, Lidia Angeleri Laking, Rosanna Šťovíček, Jan Vitória, Jorge |
| author_facet | Hügel, Lidia Angeleri Laking, Rosanna Šťovíček, Jan Vitória, Jorge |
| contents | Mutation of compact silting objects is a fundamental operation in the representation theory of finite-dimensional algebras due to its connections to cluster theory and to the lattice of torsion pairs in module or derived categories. In this paper we develop a theory of mutation in the broader framework of silting or cosilting t-structures in triangulated categories. We show that mutation of pure-injective cosilting objects encompasses the classical concept of mutation for compact silting complexes. As an application we prove that any minimal inclusion of torsion classes in the category of finitely generated modules over an artinian ring corresponds to an irreducible mutation. This generalises a well-known result for functorially finite torsion classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_02147 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mutation and torsion pairs Hügel, Lidia Angeleri Laking, Rosanna Šťovíček, Jan Vitória, Jorge Representation Theory Category Theory Rings and Algebras 18G80, 16E35 Mutation of compact silting objects is a fundamental operation in the representation theory of finite-dimensional algebras due to its connections to cluster theory and to the lattice of torsion pairs in module or derived categories. In this paper we develop a theory of mutation in the broader framework of silting or cosilting t-structures in triangulated categories. We show that mutation of pure-injective cosilting objects encompasses the classical concept of mutation for compact silting complexes. As an application we prove that any minimal inclusion of torsion classes in the category of finitely generated modules over an artinian ring corresponds to an irreducible mutation. This generalises a well-known result for functorially finite torsion classes. |
| title | Mutation and torsion pairs |
| topic | Representation Theory Category Theory Rings and Algebras 18G80, 16E35 |
| url | https://arxiv.org/abs/2201.02147 |