Colloquium October 1, 2021

Tekin Karadag, CofC

Lie Structure on Hopf Algebra Cohomology

It is known that the graded Lie bracket (Gerstenhaber bracket) structure on Hopf algebra cohomology of a quasitriangular algebra is abelian. We calculate the graded Lie bracket on Hochschild and Hopf algebra cohomologies of the Taft algebra Tp 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 Tp, as in all known quasi- triangular Hopf algebras. This example is the first known bracket computation for a nonquasi-triangular algebra.

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