Pierre Guillot

Twisting algebras using non-commutative torsors: explicit computations

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. We prove a theorem that affords a presentation by generators and relations for the algebras obtained by such twisting. We give a number of examples, including new constructions of the quantum affine spaces and the quantum tori.

Chow rings and cobordism of some Chevalley groups

We compute the cobordism rings of the classifying spaces of a certain class of Chevalley groups. In the particular case of the general linear group, we prove that it is isomorphic to the Chow ring.

Examples of Sweedler Cohomology in Positive Characteristic

There have been few examples of computations of Sweedler cohomology, or its generalization in low degrees known as lazy cohomology, for Hopf algebras of positive characteristic. In this paper we first provide a detailed calculation of the Sweedler cohomology of the algebra of functions on (ℤ/2) r , in all degrees, over a field of characteristic 2. Here the result is strikingly different from the characteristic zero analog. Then we show that there is a variant in characteristic p of the result obtained by Kassel and the author in characteristic zero, which provides a near-complete calculation of the second lazy cohomology group in the case of function algebras over a finite group; in positive characteristic, the statement is, rather surprisingly, simpler.