Lie and Jordan Algebras,
their Representations and Applications VII

dedicated to Ivan Shestakov's 70th birthday
October 23 - 28, 2017

Mini-courses

CURSOS BÁSICOS

Lucia Ikemoto Murakami e Iryna Kashuba (USP)

Introdução à teoria de representações

Resumo: Definimos as representações de estruturas algébricas básicas e exemplos clássicos. Em seguida, com mais detalhes estudamos as representações de grupos finitos e seus carácteres e as representações de álgebras de Lie complexos simples.


Alexandre Grishkov (USP)

Introdução a teoria de álgebras de Lie

Neste curso vamos estudar as algebras de Lie de dimensao finita sobre o corpo dos numeros complexos. Provamos os principais teoremsa de teoria das algebras nilpotentes (teorema de Engel ) e soluveis (teorema de Lie de Cartan). Parte principal do curso vai ser dedicada a teoria das algebras semisimles ate classificacao as ultimas. No final apresentamos as construcoes das algebras de Lie simples excepcionais.

CURSOS AVANÇADOS:

Leonid Makar-Limanov (Wayne University)

Solved and unsolved problems of affine algebraic geometry


Vladimir Sokolov (UFABC/Landau Institute)

Decompositions of loop algebras and Lax representations for integrable non-linear differential equations.

Abstract: A Lax pair is the main tool of modern theory of integrable differential equations. We consider in details Lax representations for the celebrated Korteweg-de Vries and non-linear Schroedinger equations and algebraic constructions associated with them. An algebraic version of the concept of Lax pair is a decomposition of the loop algebra over semi-simple Lie algebra G into a vector space direct sum of the subalgebra of all Taylor series and a complementary Lie subalgebra. In the case G=so(3) all possible complementary subalgebras are described. Some examples in the case G=so(n) are presented.