# Infinite dimensional Lie algebras with a structure of finitely generated modules

**Date**: Friday 20 October 2017, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Integrable Systems, Seminars, Applied Mathematics, Colloquium**Cost**: Free

#### Victor Buchstaber, Russian Academy of Sciences. Part of the algebra, geometry and integrable systems colloquia and integrable systems seminars series.

Infinite-dimensional Lie algebras with the structures of finitely generated modules naturally arise in the theory of integrable systems, algebraic geometry, differential topology, singularity theory. Fruitful examples such Lie algebras are polynomial algebras of vector fields on universal bundles of Jacobians of hyperelliptic curves and automorphic Lie algebras. Witt algebra, Kac - Moody algebras and other classical infinite-dimensional Lie algebras have the faithful representations in a number of important examples of such Lie algebras.

The talk is devoted to the problems of general theory and applications of the infinite-dimensional Lie algebras with the structures of finitely generated modules. We discuss the general constructions of such algebras and their morphisms. Important examples will be given and their connections with known infinite-dimensional Lie algebras described.

This work is in collaboration with A V Mikhailov.

**Victor Buchstaber,** *Russian Academy of Sciences*