On the Hochschild cohomology of tame Hecke algebras

We explicitly calculate a projective bimodule resolution for a special biserial algebra giving rise to the Hecke algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal H}_q(S_4)}$$\end{document} when q = −1. We then determine the dimensions of the Hochschild cohomology groups.