Posted May 17, 20153:30 pm - 4:20 pm Lockett 235
Cris Negron, University of Washington
Braided structures and the Gerstenhaber bracket on Hochschild cohomology
Given a finite dimensional Hopf algebra H acting on an algebra A, we can form an intermediate cohomology H˙(H, A) which comes equipped with a natural right H-action, and recovers the Hochschild cohomology of the smash product A#H after taking invariants. In fact, the cohomology H˙(H, A) is a Yetter-Drinfeld module over H and is a braided commutative algebra under the natural braiding induced by the Yetter-Drinfeld structure. This multiplicative structure has proved useful in verifying finite generation of Hopf cohomology, and has been studied extensively by Forest-Greenwood, Shepler, and Witherspoon. Supposing H has finite exponent, I will discuss how one can produce a braided antisymmetric bracket on H˙(H, A) which lifts the Gerstenhaber bracket to this braided setting, in the sense that it recovers the Gerstenhaber bracket after taking invariants.