Mathematics Algebra Seminar. Nulan Ismailov, On the Variety of Right-Symmetric Algebras
This event is in the past.
When:
November 21, 2023
1 p.m. to 2 p.m.
1 p.m. to 2 p.m.
Where:
Nelson Library, Faculty Admin Building
#1146
Event category:
Seminar
In-person
Speaker: Nurlan Ismailov
Institution: Astana IT University, Astana, Kazakhstan
Title: On the variety of right-symmetric algebras
Abstract: The problem of the existence of a finite basis of identities for a variety of associative algebras over a field of characteristic zero was formulated by Specht in 1950. We say that a variety of algebras has the Specht property if any of its subvariety has a finite basis of identities. In 1988, A. Kemer proved that the variety of associative algebras over a field of characteristic zero has the Specht property. Specht's problem has been studied for many well-known varieties of algebras, such as Lie algebras, alternative algebras, right-alternative algebras, and Novikov algebras.
An algebra is called right-symmetric if it satisfies the identity (a, b, c) = (a, c, b) where (a, b, c) = (ab)c − a(bc) is the associator of a, b, c.
The talk is devoted to the Specht problem for the variety of right-symmetric algebras. It is proved that the variety of right-symmetric algebras over an arbitrary field does not satisfy the Specht property.
The talk is based on the results of joint work with U. Umirbaev.
Time: Tuesday, November 21, 1-2 pm.
Location: Nelson Room, 1146 FAB