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Specht Problem and Noncommutative Algebraic Geometryтезисы доклада
- Автор: Belov Alexei
- Сборник: Department of Mathematics and Computer Science, Mathematics Colloquium. Sunday, May 21 at 12:00. see also http://www2.math.technion.ac.il/ techm/20000521120020000521bel
- Тезисы
- Год издания: 2000
- Место издания: Bar-Ilan Univerity
- Первая страница: .
- Аннотация: 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.
- Добавил в систему: Белов Алексей Яковлевич