Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies

We calculate the Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies of the Taft algebra T-p for any integer p > 2 which is a nonquasi-triangular Hopf algebra. We show that the bracket is indeed zero on Hopf algebra cohomology of T-p, as in all known quasi-triangular Hopf algebras. This example is the first known bracket computation for a nonquasi-triangular algebra. Also, we find a general formula for the bracket on Hopf algebra cohomology of any Hopf algebra with bijective antipode on the bar resolution that is reminiscent of Gerstenhaber's original formula for Hochschild cohomology. (C) 2021 Elsevier B.V. All rights reserved.