In September 2000, at the Centre de Recerca Matematica in Barcelona, we pre sented a 30-
hour Advanced Course on Algebraic Quantum Groups. After the course, we expanded and …

Murray Gerstenhaber Samuel D. Schack This paper is an expanded version of remarks
delivered by the authors in lectures at the June, 1990 Amherst conference on Quantum …

Deformation quantization, which gives a development of quantum mechanics independent
of the operator algebra formulation, and quantum groups, which arose from the inverse …

We construct a class of compact quantum groups, by strict deformation quantization of
compact Lie groups within the C*-algebra setting. These deformations come from Poisson …

Let G be a Lie group. For any Abelian subalgebra h of the Lie algebra g of G, and any r ∈ h
Λ h, the difference of the left and right translates of r gives a compatible Poisson bracket on …

Given a Hopf algebra A, there exist various cohomology theories for the category of Hopf
bimodules over A, introduced by M. Gerstenhaber and SD Schack, and by C. Ospel. We …

The twin group TW n on n strands is the group generated by t 1,…, tn− 1 with defining
relations ti 2= 1, titj= tjti if| i− j|> 1. We find a new instance of semisimple Schur–Weyl duality …

We compute explicitly the bialgebra cohomology of the duals of the generalized Taft
algebras, which are noncommutative, noncocommutative finite-dimensional Hopf algebras …

Permutation modules are fundamental in the representation theory of symmetric groups and
their corresponding Iwahori–Hecke algebras ℋ= ℋ (). We find an explicit combinatorial basis …

Let M*(C) denote the C∗-algebra defined as the direct sum of all matrix algebras {Mn (C):
n⩾ 1}. It is known that M*(C) has a non-cocommutative comultiplication Δφ. From a certain …