Extriangulated structures from stability conditions and application to braid representations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911325586718720 |
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| author | Queffelec, Hoel Thiel, Anne-Laure Wagner, Emmanuel |
| author_facet | Queffelec, Hoel Thiel, Anne-Laure Wagner, Emmanuel |
| contents | We use the notion of Bridgeland stability condition and its associated metric to endow triangulated categories with extriangulated structures and study their extriangulated Grothendieck groups. This study is motivated by Khovanov-Seidel's categorification of the Burau representation, from which can be extracted the Lawrence-Krammer-Bigelow representation, providing a relation between these two faithful representations of the braid groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_16142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extriangulated structures from stability conditions and application to braid representations Queffelec, Hoel Thiel, Anne-Laure Wagner, Emmanuel Quantum Algebra Group Theory Representation Theory 18G80, 20F36, 18F30, 18G35 We use the notion of Bridgeland stability condition and its associated metric to endow triangulated categories with extriangulated structures and study their extriangulated Grothendieck groups. This study is motivated by Khovanov-Seidel's categorification of the Burau representation, from which can be extracted the Lawrence-Krammer-Bigelow representation, providing a relation between these two faithful representations of the braid groups. |
| title | Extriangulated structures from stability conditions and application to braid representations |
| topic | Quantum Algebra Group Theory Representation Theory 18G80, 20F36, 18F30, 18G35 |
| url | https://arxiv.org/abs/2512.16142 |