Department of Mathematics University of Haifa ALGEBRA SEMINAR Speaker: Mr. Ofir David (Technion) Date: Monday, November 5th, 2012 at12:00(Please note slightly earlier time than previously announced.) Place: Room 614 of the Science & Education Building, Univ. of Haifa Title: Regular G-Graded Algebras Abstract: The infinite Grassmann algebra E (exterior algebra) plays a vital role in many parts of mathematics. One of its most important property is that with its standard Z_2 grading E=E_0 + E_1, this algebra satisfies the equation xy=(-1)^(deg(x)deg(y)) yx where deg(x) [=0 or 1] denotes the degree of x. Regev and Seeman generalized this property as follows: Let G be a finite abelian group. Then a G-grading on an algebra A is called regular if 1. for any a_g,b_h with degrees g, h respectively we have a_g b_h =theta(g,h) b_h a_g where theta(g,h) is a nonzero scalar. 2. for every g_1,...,g_n there are a_i in A of degrees g_i respectively such that a_1*a_2*...*a_n != 0. In order to study these algebras, Bahturin and Regev defined when a regular G-grading on A is minimal. The grading is called minimal if for any g!=e in G there is some h in G such that theta(g,h)!=1. Bahturin and Regev then conjectured that the size |G| for a minimal regular grading on A is an invariant of A. In this talk we give a positive answer to this conjecture. We do this by considering the (graded) polynomial identities of A, where the size |G| is an invariant of the ideal of polynomial identities of A. This is a joint work with Prof. Eli Aljadeff. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ofir Schnabel <os2519@yahoo.com>