Modular categories associated with unipotent groups

Making nontrivially associated modular categories from finite groups

We show that the double of the nontrivially associated tensor category constructed from left coset representatives of a subgroup of a finite group X is a modular category. Also we give a definition of the character of an object in this category as an element of a braided Hopf algebra in the category. This definition is shown to be adjoint invariant and multiplicative on tensor products. A detai...

Cluster Structures for 2-calabi-yau Categories and Unipotent Groups

We investigate cluster tilting objects (and subcategories) in triangulated 2-Calabi-Yau categories and related categories. In particular we construct a new class of such categories related to preprojective algebras of non Dynkin quivers associated with elements in the Coxeter group. This class of 2-Calabi-Yau categories contains the cluster categories and the stable categories of preprojective ...

From Quantum Groups to Unitary Modular Tensor Categories

Modular tensor categories are generalizations of the representation theory of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFT and invariants of 3-manifolds. Although other constructions have since been found, quantum groups remain the most prolific source. Recently proposed applications to quantum computing have provided an impetus to underst...

Heisenberg Idempotents on Unipotent Groups

Let G be a possibly disconnected algebraic group over an algebraically closed field k of characteristic p > 0, such that its neutral connected component, H = G0, is a unipotent group. We recall that an algebraic group over k is defined to be a smooth group scheme of finite type over k. Let us fix a prime number l 6= p. If X is a k-scheme, we use D(X) to denote the bounded derived category of Ql...

1 9 Ja n 20 07 Cluster structures for 2 - Calabi - Yau categories and unipotent groups