no. 3
Extriangulated structures from stability conditions and application to braid representations
Queffelec, Hoel1 ; Thiel, Anne-Laure2; Wagner, Emmanuel3
1France-Australia Mathematical Sciences and Interactions ANU – CNRS International Research Laboratory, Australia
2Université Bourgogne Europe, CNRS, IMB UMR 5584, 21000 Dijon, France
3Univ Paris Cité, IMJ-PRG, Univ Paris Sorbonne, UMR 7586 CNRS, F-75013, Paris, France
Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 371-398

We use the notion of Bridgeland stability condition and an associated rank function 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.

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DOI: 10.5802/art.44
Classification: 18G80, 20F36, 18F30, 18G35
Keywords: Extriangulated categories, braid groups, LKB representations

Queffelec, Hoel  1 ; Thiel, Anne-Laure  2 ; Wagner, Emmanuel  3

1 France-Australia Mathematical Sciences and Interactions ANU – CNRS International Research Laboratory, Australia
2 Université Bourgogne Europe, CNRS, IMB UMR 5584, 21000 Dijon, France
3 Univ Paris Cité, IMJ-PRG, Univ Paris Sorbonne, UMR 7586 CNRS, F-75013, Paris, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Queffelec, Hoel; Thiel, Anne-Laure; Wagner, Emmanuel. Extriangulated structures from stability conditions and application to braid representations. Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 371-398. doi: 10.5802/art.44
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