Department of Mathematics          University of Haifa
 
                     ALGEBRA  SEMINAR
 
Speaker: Mr. Ofir David (Technion)
 
Date: Monday, November 5th, 2012 at 12:00 
(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.
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Ofir Schnabel   <os2519@yahoo.com>