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Polynomial identities and numerical invariants

Grant number: 19/02510-2
Support type:Research Grants - Visiting Researcher Grant - International
Duration: July 03, 2019 - 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
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil


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)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
SHESTAKOV, I.; ZAICEV, M. Eventually non-decreasing codimensions of {*}-identities. ARCHIV DER MATHEMATIK, v. 116, n. 4 JAN 2021. Web of Science Citations: 0.

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