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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.05140 |
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| _version_ | 1866908635870789632 |
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| author | Bellamy, Gwyn Castellan, Simone Goodbody, Isambard |
| author_facet | Bellamy, Gwyn Castellan, Simone Goodbody, Isambard |
| contents | Motivated by the representation theory of symplectic reflection algebras, deformed preprojective algebras, and graded Hecke algebras, we consider filtered algebras $U$ whose associated graded is Koszul. The Koszul dual of $U$, as defined by Positselski, is a curved dg-algebra. We establish an exact equivalence between the unbounded derived category of $U$ and an explicit quotient of the homotopy category of injective modules over the dual curved dg-algebra. This recovers a special case of a result of Positselski. In the case where $U$ has finite global dimension, the quotient is trivial and hence the unbounded derived category of $U$ is equivalent to the homotopy category of injective modules over the dual curved dg-algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05140 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-homogeneous Koszul duality in representation theory Bellamy, Gwyn Castellan, Simone Goodbody, Isambard Representation Theory Rings and Algebras 16S37 (Primary) 16D90, 18G80, 20C08 (Secondary) Motivated by the representation theory of symplectic reflection algebras, deformed preprojective algebras, and graded Hecke algebras, we consider filtered algebras $U$ whose associated graded is Koszul. The Koszul dual of $U$, as defined by Positselski, is a curved dg-algebra. We establish an exact equivalence between the unbounded derived category of $U$ and an explicit quotient of the homotopy category of injective modules over the dual curved dg-algebra. This recovers a special case of a result of Positselski. In the case where $U$ has finite global dimension, the quotient is trivial and hence the unbounded derived category of $U$ is equivalent to the homotopy category of injective modules over the dual curved dg-algebra. |
| title | Non-homogeneous Koszul duality in representation theory |
| topic | Representation Theory Rings and Algebras 16S37 (Primary) 16D90, 18G80, 20C08 (Secondary) |
| url | https://arxiv.org/abs/2511.05140 |