Please Enter Keywords
资源 63
[Lecture] Subalgebras of free algebras
Jan. 05, 2023
Speaker: Vladimir Dotsenko, University of Strasbourg

Time: 16:00-17:00 pm, January 5, 2023, GMT+8

Venue: Zoom Meeting ID: 904 645 6677 Password:2023


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.


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.

Source: SRMC