Hochschild Cohomology of Smash Products and Rank One Hopf Algebras

Gorenstein global dimensions for Hopf algebra actions

Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra‎. ‎In this paper‎, ‎we investigate Gorenstein global dimensions for Hopf‎ ‎algebras and twisted smash product algebras $Astar H$‎. ‎Results from‎ ‎the literature are generalized‎. 

Current Research: Noncommutative Representation Theory

Group actions are ubiquitous in mathematics. To understand a mathematical object, it is often helpful to understand its symmetries as expressed by a group. For example, a group acts on a ring by automorphisms (preserving its structure). Analogously, a Lie algebra acts on a ring by derivations. Unifying these two types of actions are Hopf algebras acting on rings. A Hopf algebra is not only an a...

Second Hochschild Cohomology of Convolution Algebras

On the Cohomology of a Smash Product of Hopf Algebras

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

Hopf Algebras in Renormalization Theory: Locality and Dyson-schwinger Equations from Hochschild Cohomology

In this review we discuss the relevance of the Hochschild cohomology of renormalization Hopf algebras for local quantum field theories and their equations of motion. CONTENTS Introduction and acknowledgments 1 1. Rooted trees, Feynman graphs, Hochschild cohomology and local counterterms 2 1.1. Motivation 2 1.2. Basic definitions and notation 4 1.3. The Hopf algebra of rooted trees 4 1.4. Tree-l...