Highest weight categories and stability conditions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911457523793920 |
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| author | Cipriani, Alessio Woolf, Jon |
| author_facet | Cipriani, Alessio Woolf, Jon |
| contents | Highest weight categories are an abstraction of the representation theory of semisimple Lie algebras introduced by Cline, Parshall and Scott in the late 1980s. There are by now many characterisations of when an abelian category is highest weight, but most are hard to verify in practice. We present two new criteria - one numerical in terms of the Grothendieck group, and one in terms of Bridegland stability conditions - which are easier to verify. The stability criterion naturally generalises to a characterisation of properly stratified categories. The numerical criterion implies a criterion of Green and Schroll for when modules over a monomial algebra are highest weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13728 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Highest weight categories and stability conditions Cipriani, Alessio Woolf, Jon Representation Theory Highest weight categories are an abstraction of the representation theory of semisimple Lie algebras introduced by Cline, Parshall and Scott in the late 1980s. There are by now many characterisations of when an abelian category is highest weight, but most are hard to verify in practice. We present two new criteria - one numerical in terms of the Grothendieck group, and one in terms of Bridegland stability conditions - which are easier to verify. The stability criterion naturally generalises to a characterisation of properly stratified categories. The numerical criterion implies a criterion of Green and Schroll for when modules over a monomial algebra are highest weight. |
| title | Highest weight categories and stability conditions |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2410.13728 |