  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.

Quantum Algebra;K-Theory and Homology;Rings and Algebras;Representation Theory