THE TALK WILL START AT 11:00.

Department of Mathematics                  University of Haifa

ALGEBRA  SEMINAR

Speaker: Mr. Ofir Schnabel (University of Haifa)

Date: Wednesday, May 16th, 2012 at 11:00
**(NOTE THE CHANGE)**

Place: Room 614 of the Science & Education Building, Univ. of
Haifa

Title: Refinements of the universal covering property for
complex matrix algebras

Abstract:

A theorem of Bahturin and Zaicev says that any fine strong
$G$-grading of $M_n(\mathbb{C})$ is induced by a twisted group
algebra $\mathbb{C}^fG$, where $G$ is a group of central type
of order $n^2$, e.g. $C_n\times C_n$, and $[f]\in H^2(G,\mathbb{C})$ is nondegenrate. Any such twisted group
algebra determines a simply connected grading of
$M_n(\mathbb{C})$. In a recent paper, Cibils, Redondo and
Solotar show that for any $n$ there is another simply
connected grading of $M_n(\mathbb{C})$, namely by the free
group $F_{n-1}$. Consequently there is no universal covering
of $M_n(\mathbb{C})$. In this talk we discuss the question
whether the existence of a universal covering of
$M_n(\mathbb{C})$ can be disproved using only fine strong