A braid group action on an $A_\infty$-category for zigzag algebras
Quantum Algebra
2023-05-05 v1 K-Theory and Homology
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 -differential graded structures by a version of Koszul duality. We prove that the minimal model -structure on the zigzag algebras is {\em not} formal. We construct a braid group action in this setting and suggest a symplectic interpretation.
Keywords
Cite
@article{arxiv.2305.02824,
title = {A braid group action on an $A_\infty$-category for zigzag algebras},
author = {Benjamin Cooper and You Qi and Joshua Sussan},
journal= {arXiv preprint arXiv:2305.02824},
year = {2023}
}
Comments
32 pages, 2 figures. Dedicated to Igor Frenkel on the occasion of his seventieth birthday. Comments welcome. arXiv admin note: text overlap with arXiv:1312.7692