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Sino-Russian Mathematics Center-JLU Colloquium(2023-001)—Subalgebras of free algebras

Posted: 2023-03-13   Views: 

报告题目:Subalgebras of free algebras

报 告 人:Vladimir Dotsenko

所在单位:University of Strasbourg

报告时间:2023年1月5日 16:00-18:00

报告地点:ZOOM Id:904 645 6677,Password:2023


报告摘要: A classical result going back to works of Shirshov and Witt in 1950s states that every subalgebra of the free Lie algebra is free. Understanding what makes a variety of algebras satisfy this property has been an important open question in ring theory, recorded, for instance, in the Dniester Notebook. I shall talk about a recent work with Ualbai Umirbaev in which we developed a method that allowed us to exhibit infinitely many varieties of algebras (with one binary operation) satisfying this property; prior to our work, only six such varieties had been known. One surprising consequence of our work is that for the variety of all right-symmetric algebras subalgebras of free algebras are free.

报告人简介:Vladimir Dotsenko is a professor at the University of Strasbourg, France. His work applies ideas of category theory to concrete questions of algebra, combinatorics, geometry and topology.