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DOS SANTOS, F. A. Representations of Heisenberg subálgebras of KricheverNovikov algebras. 2017. 64 f. Dissertação (Mestrado) Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, 2017. This work presents, in a summarized format, two years of study under the advisoring of professor Vyacheslav Futorny. During this period of time, the author was able to be in touch with the cientific comunity working in Lie algebras and their representations, and to do his first original contributions on Lie algebras as well. The author has also dedicated to the study of preliminary material and to a first contact with research articles and recent publications. From February to July, 2016, the author was a research intern at Université Laval (Québec) under the supervision of professor Michael Lau, and could produce a significant portion of this dissertation. The main results of this work were reached in collaboration with both Professor Futorny and Professor Lau. This work gives an introduction to the already known Krichever-Novikov algebras limited only to the examples approached before in [Bre95], [Cox08], [CJ13],[CFM14] and [BCF09], and the structures definitions that could help us to study these spaces, including affine Lie algebras, loop algebras and Verma modules. Let K be a 4-point, 3-point, elliptic or DJKM Krichever-Novikov algebra and its respective Heisenberg subalgebras K̂ = K ⊗ hK , where hK is the K Cartan subalgebra. In the Theorems 3.2.3, 3.4.3, 3.6.3 and 3.8.3 we will give a explicit irreducibility criteria for φ-Verma K̂ -modules MK̂ ,φ

Módulos irredutíveis para subálgebras de Heisenberg de álgebras de Krichever-Novikov