Murray Gerstenhaber constructed a graded Lie structure (Gerstenhaber bracket) on Hochschild cohomology, which makes Hochschild cohomology a Lie algebra. However, it is not easy to calculate bracket structure with the original definition. There is an alternative technique to compute Gerstenhaber bracket on Hochschild cohomology, introduced by Chris Negron and Sarah Witherspoon. It is also known that Hopf algebra cohomology has a bracket and the bracket is trivial when a Hopf algebra is quasi-triangular. We use a similar technique to the technique given by Negron and Witherspoon to calculate the Lie structure on Hochschild cohomology of the Taft algebra Tp for any integer p>2 which is a nonquasi-triangular Hopf algebra. Then, we find the corresponding bracket on Hopf algebra cohomology of Tp. We show that the bracket is indeed zero on Hopf algebra cohomology of Tp, as in all known quasi-triangular Hopf algebras. This example is the first known bracket computation for a nonquasi triangular algebra.
This is the second part of two talks, the first of which may be found here.
This video is part of the University of Georgia‘s Algebra seminar.
