Report Title：Subalgebras of free algebras
Reporter：Vladimir Dotsenko
Institution：University of Strasbourg
Time：January,5,2023 16:00-18:00
Location：ZOOM Id：904 645 6677，Password：2023
Meeting link：https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09
Abstract : 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.
Introduction of the Reporter：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.
