The second author constructed a topological ribbon Hopf algebra from the unrolled quantum group associated with super Lie sl(2|1). We generalize this fact to context of groups and construct algebras. Then we use such an algebra, discrete Fourier transforms, symmetrized graded integral modified trace define Hennings invariant 3-manifolds endowed cohomology class which contains graph. Finally, no...

s printed May 21, 2011 Sanghoon Baek (UNIVERSITY OF OTTAWA) Essential dimension of simple algebras and its application to algebraic groups of type An In this talk, we introduce the notion of essential dimension of an algebraic structure and discuss some recent results on the essential dimension of certain classes of central simple algebras. We also relate these results to the essential dimensio...

From the point of view of homotopy theory a compact Lie group G has the following remarkable combination of properties: (1) G can be given the structure of a finite CW-complex, and (2) there is a pointed space BG and a homotopy equivalence from G to the loop space QB G . Of course the space BG in (2) is the ordinary classifying space of G. In general, a finite complex X together with a chosen e...

We introduce and study the notion of representation up to homotopy of a Lie algebroid, paying special attention to examples. We use representations up to homotopy to define the adjoint representation of a Lie algebroid and show that the resulting cohomology controls the deformations of the structure. The Weil algebra of a Lie algebroid is defined and shown to coincide with Kalkman’s BRST model ...

Introduction 2 1. Preliminaries on conformal algebras and modules 4 2. Basic definitions 9 3. Extensions and deformations 13 4. Homology 17 5. Exterior multiplication, contraction, and module structure 18 6. Cohomology of conformal algebras and their annihilation Lie algebras 19 6.1. Cohomology of the basic complex 19 6.2. Cohomology of the reduced complex 21 6.3. Cohomology of conformal algebr...

We give a general construction of rings graded by the conjugacy classes of a finite group. Some examples of our construction are the Hochschild cohomology ring of a finite group algebra, the Grothendieck ring of the Drinfel’d double of a group, and the orbifold cohomology ring for a global quotient. We generalize the first two examples by deriving product formulas for the Hochschild cohomology ...