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 gradings. A joint work with Y. Ginosar. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: YUVAL GINOSAR <ginosar@math.haifa.ac.il>