# Current Seminar

**April 16 and April 23, 2014**

Yuri Bahturin (MUN) "Locally finite Lie algebras"

Abstract. An algebra 𝐴 over a field 𝐹 is called locally finite if any finite set of elements of 𝐴 is contained in a finite-dimensional subalgebra. Equivalently, 𝐴 is the direct limit of a family of finite-dimensional algebras. A hard (essentially, wild) problem that remains open is to classify simple locally finite algebra (associative, Lie, etc.) A complete classification of locally finite simple Lie algebras, due to Baranov-Zhilinski, exists in the case of so-called diagonal direct limits over algebraically closed field of characteristic zero. Even better known (fields of positive characteristic included!) are so-called finitary simple Lie algebras (Baranov-Strade). In this latter case we can even classify all graded simple algebras (Bahturin-Kochetov-Zaicev).

In this talk I would like to discuss basic notions of the theory of locally finite Lie algebras and try to explain current state of the problem of classifying group grad-ings on the diagonal direct limits of classical simple Lie algebras.

*HH-3017 at 1:00 p.m.*