A braid group action on a \(p\)-DG homotopy category (Q2667918)

A categorification of the braid group action on the Burau representation at a prime root of unity was constructed in [\textit{Y. Qi} and \textit{J. Sussan}, Sel. Math., New Ser. 22, No. 3, 1157--1193 (2016; Zbl 1345.81061)]. Partially motivated by this construction, in [\textit{M. Khovanov} and \textit{J. Sussan}, J. Pure Appl. Algebra 222, No. 8, 1957--2000 (2018; Zbl 1418.16026)], the authors considered a deformation \(W = W(n, 1)\) of \(A^{!}_{n}\) and showed that there is a categorical braid group action on the homotopy category of \(W\)-modules. Later, this result was extended to a categorical braid group action on the homotopy category of a deformation of more general Webster algebras for \(\mathfrak{sl}_{2}\). In the current paper the authors return to the simplified setting of \(W\) and showed that there is a categorical action of the braid group on \(n\) strands on the relative \(p\)-DG homotopy category of \(W\).