Department of

October 2019November 2019December 2019 Su Mo Tu We Th Fr Sa Su Mo Tu WeThFr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 5 1 2 1 2 3 4 5 6 7 6 7 8 9 10 11 12 3 4 5 6 7 8 9 8 9 10 11 12 13 14 13 14 15 16 17 18 19 10 11 12 13 14 15 16 15 16 17 18 19 20 21 20 21 22 23 24 25 26 17 18 19 202122 23 22 23 24 25 26 27 28 27 28 29 30 31 24 25 26 27 28 29 30 29 30 31

Friday, November 8, 2019

**Abstract:** In studies of finite-dimensional Hopf algebras one makes consistent use of a number of standard operations. The most fundamental of these operations include linear duality, (cocycle) deformation, and twisting by so-called Drinfeld twists. Many numerical invariants of Hopf algebras are known to be stable under these operations. However, one can see from examples, that the cohomology ring H*(A,k) for a finite-dimensional Hopf algebra A with trivial coefficients is not preserved under deformation or duality of A. In joint work with J. Plavnik we conjecture that, although the cohomology ring itself may vary, the Krull dimension of cohomology should be invariant under a general class of ``duality operations" which includes linear duality, deformation, and Drinfeld twisting. I this talk I will give the necessary definitions and examples, discuss the aforementioned conjecture, and provide some positive results obtained jointly with J. Plavnik.