专家报告

题      目：Polynomial identities in Novikov and right-symmetric

algebras

报  告  人：Nurlan Ismailov 教授 (邀请人：张泽锐)

                                      Astana IT University

时      间： 11月22日  16：20-16:50

地     点：数科院西楼111报告厅

报告人简介:

        Nurlan Ismailov, an Associate Professor at Astana IT University, Astana, Kazakhstan. He obtained PhD in 2015 under the supervision of Prof. Askar Dzhumadil’daev. In 2018, he held a postdoctoral position at the University of São Paulo, São Paulo, Brazil, under the supervision of Prof. Ivan Shestakov. His research area is nonassociative algebras and their polynomial identities. He has 18 scientific papers.

摘      要：

       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, and right-alternative 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. Right-symmetric algebra that satisfies the additional identity a(bc) = b(ac) is called Novikov algebra.

The talk is devoted polynomial identities in Novikov algebras and the Specht problems for the varieties of Novikov and right-symmetric algebras. We prove that every Novikov algebra satisfying a nontrivial polynomial identity over a field of characteristic zero is right-associator nilpotent. An analogous, simpler statement is also proved for commutative differential algebras. We also establish that the variety of Novikov algebras over a field of characteristic zero has the Specht property. However, 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 V. Dotsenko and U. Umirbaev.

        欢迎老师、同学们参加、交流！