Department of Mathematics University of Haifa
Algebra Seminar
Speaker: Prof. Alexei Belov-Kanel (Bar-Ilan)
Topic: Specht type problems and noncommutative algebraic geometry.
Date: Tuesday, January 13th, 2004
Place: Room 614 (1621) on the 6th floor of the Science & Education
Building (opposite the main building), University of Haifa.
Time: 4:10 PM
Abstract:
The general Specht problem says "does given set of identities of
associative algebras stabilize? i.e. does any set of identities can be
deduced from finite subset?
Specht kept in mind case of field of characteristic zero, and this
problem was solved by A.R.Kemer in affirmative way. In positive
characteristics for case of finite number of variables A.Belov gave an
affirmative answer and in general counterexamples was constructed.
The general Specht problem is one of the central problems in polynomial
identity theory. It solution gave a technique related with some point of
view on noncommutative algebraic geometry and representation theory to
solve some other open questions, for example to prove that noetherian
affine PI-algebras are finitely presented and to prove the rationality
of Hilbert series of relatively free algebras.
The counterexamples in positive characteristics and Kemers proof of
finite basis property in characteristic zero connected with some deep
properties of Grassman algebra and, by the way, give us a chance to
built a supertheory in characteristic 2.
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Technion Math Net-2 (TECHMATH2)
Editor: Eddy Mayer-Wolf
Announcement from: Yuval Ginosar