Book chapter
A braid group action on an A∞-category for zigzag algebras
From Representation Theory to Mathematical Physics and Back, pp.119-144
Contemporary Mathematics, v. 817, American Mathematical Society
2025
DOI: 10.1090/conm/817/16323
Abstract
We construct differential graded enhancements of the zigzag algebras which were used by Khovanov, Seidel and Thomas to produce categorical braid group actions. These enhancements are related to p-differential graded structures by a version of Koszul duality. We prove that the minimal model A∞-structure on the zigzag algebras is not formal. We construct a braid group action in this setting and suggest a symplectic interpretation
Details
- Title: Subtitle
- A braid group action on an A∞-category for zigzag algebras
- Creators
- Benjamin Cooper - Department of Mathematics, University of Iowa, Iowa City, Iowa, 52242You Qi - University of VirginiaJoshua Sussan
- Contributors
- Mikhail Khovanov (Editor) - Johns Hopkins UniversityJoshua Sussan (Editor) - CUNY Medgar Evers, Brooklyn, NYAnton Zeitlin (Editor) - Louisiana State University
- Resource Type
- Book chapter
- Publication Details
- From Representation Theory to Mathematical Physics and Back, pp.119-144
- Publisher
- American Mathematical Society; Providence, Rhode Island
- Series
- Contemporary Mathematics; v. 817
- DOI
- 10.1090/conm/817/16323
- eISSN
- 1098-3627
- ISSN
- 0271-4132
- Number of pages
- 26
- Language
- English
- Date published
- 2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984824299202771
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