We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by Andruskiewitsch and Schneider of such Hopf algebras. Examples include all of Lusztig's small quantum groups, whose… (More)
We give explicit formulas for maps in a long exact sequence connecting bialgebra cohomology to Hochschild cohomology. We give a sufficient condition for the connecting homomorphism to be surjective. We apply these results to compute all bialgebra two-cocycles of certain Radford biproducts (bosoniza-tions). These two-cocycles are precisely those associated… (More)
The purpose of this paper is to introduce a cohomology theory for abelian matched pairs of Hopf algebras and to explore its relationship to Sweedler cohomology, to Singer cohomology and to extension theory. An exact sequence connecting these cohomology theories is obtained for a general abelian matched pair of Hopf algebras, generalizing those of Kac and… (More)
A five term sequence for the low degree cohomology of a smash product of (cocommutative) Hopf algebras is obtained, generalizing that of Tahara for a semi-direct product of groups 0 Introduction Our aim is to obtain a five term sequence for the cohomology of a smash product of (cocommutative) Hopf algebras, which generalizes the Tahara sequence for a… (More)
Let k be a positive integer and let G k denote the set of all joint distributions of k-tuples (a 1 ,. .. , a k) in a non-commutative probability space (A, ϕ) such that ϕ(a 1) = · · · = ϕ(a k) = 1. G k is a group under the operation of free multiplicative convolution ⊠. We identify G k , ⊠ as the group of characters of a certain Hopf algebra Y (k). Then, by… (More)
We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language L, find a maximal independent language containing L. We consider the case where the code-related property is defined via a rational binary relation that is decreasing with respect to any fixed total order on the set of words. Our… (More)
This document is an extended abstract of the paper 'Hopf algebras and the logarithm of the S-transform in free probability' in which we introduce a Hopf algebraic approach to the study of the operation (free multiplicative convolution) from free probability.
Schedule Abstracts of Talks Rooms All talks will be delivered in Room SN-3060 (Science Building). Coffee breaks/discussions will be in Coffee Room of the Department of Mathematics and Statistics HH-3022 (Henrietta Harvey Building). You are always welcome to visit the office of Atlantic Algebra Centre at HH-2010.
We introduce and study bimeasurings from pairs of bialge-bras to algebras. It is shown that the universal bimeasuring bialgebra construction, which arises from Sweedler's universal measuring coalgebra construction and generalizes the finite dual, gives rise to a contravariant functor on the category of bialgebras adjoint to itself. An interpretation of… (More)