Connected Hopf Algebras with Dixmier Basis and Infinite Primary Decomposition

Connected Hopf Algebras with Dixmier Bases and Infinite Primary Decomposition

Titles and Abstracts for the Algebra Extravaganza

Title: The Dixmier-Moeglin equivalence for D-groups Abstract: The Dixmier-Moeglin equivalence is a characterization of the primitive ideals of an algebra that holds for many classes of rings, including affine PI rings, enveloping algebras of finite-dimensional Lie algebras, and many quantum algebras. For rings satisfying this equivalence, it says that the primitive ideals are precisely those pr...

On the Hopf algebra of functional graphs and differential algebras

We develop the Hopf algebraic structure based on the set of functional graphs, which generalize the case of the forests of rooted trees. We use noncommutative polynomials as generating monomials of functional graphs and we introduce several kinds of brackets in accordance with the decomposition in connected components of the graph of a mapping of a finite set into itself, i.e. basins of attract...

Renormalization in connected graded Hopf algebras: an introduction

We give an account of the Connes-Kreimer renormalization in the context of connected graded Hopf algebras. We first explain the Birkhoff decomposition of characters in the more general context of connected filtered Hopf algebras, then specializing down to the graded case in order to introduce the notions of locality, renormalization group and Connes-Kreimer’s Beta function. The connection with ...

ALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS

Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...