Graded polynomial identities and identity with trace, and invariant theory
Vesselin Stoyanov Drensky | Institute of Mathematics Bulgarian Academy of Sciences...
| Grant number: | 19/02510-2 |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| Start date: | July 03, 2019 |
| End date: | August 30, 2019 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Algebra |
| Principal Investigator: | Ivan Chestakov |
| Grantee: | Ivan Chestakov |
| Visiting researcher: | Mikhail Vladimirovich Zaicev |
| Visiting researcher institution: | Lomonosov Moscow State University (MSU), Russia |
| Host Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
Abstract
One of the mail ojectives of our project is to show how one can combine methods of the ring theory, combinatorics and representation theory of grouds with analytical approach in order to study polynomial identities of associative and non-associative algebras. In our project we shall be mostly concerned with algebras whose sequence of codimensions is exponentially bounded. One of the problem is an open question: is it true that after joining external unit to algebra its PI-exponent either increase to 1 or not change. This conjecture was confirmed in many partial cases. We plan to extend already known results to graded codimensions. The second direction of our project is the attempt to give estimation of values of non-graded and graded PI-exponents of certain Lie and Jordan superalgebras. (AU)
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