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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.15466 |
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| _version_ | 1866916029291036672 |
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| author | Amiot, Claire Plamondon, Pierre-Guy |
| author_facet | Amiot, Claire Plamondon, Pierre-Guy |
| contents | We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\infty$-category and let it play the role of the partially wrapped Fukaya category of an orbifold surface. We classify indecomposable objects in terms of graded curves with signs, or taggings, at orbifold points. We compute morphisms between a class of objects, and we use this to describe tilting objects and find algebras derived-equivalent to skew-gentle algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Skew-group $A_{\infty}$-categories as Fukaya categories of orbifolds Amiot, Claire Plamondon, Pierre-Guy Representation Theory 16E35, 16G10 We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\infty$-category and let it play the role of the partially wrapped Fukaya category of an orbifold surface. We classify indecomposable objects in terms of graded curves with signs, or taggings, at orbifold points. We compute morphisms between a class of objects, and we use this to describe tilting objects and find algebras derived-equivalent to skew-gentle algebras. |
| title | Skew-group $A_{\infty}$-categories as Fukaya categories of orbifolds |
| topic | Representation Theory 16E35, 16G10 |
| url | https://arxiv.org/abs/2405.15466 |