Representations of non-associative algebras and superalgebras

• Grant number: 16/08740-1
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2016
• End date: July 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Iryna Kashuba
• Grantee: Iryna Kashuba
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project in area of Algebra and consists of the following parts. In first one, the main goal is to study the categories of indecomposable representations of finite dimension over Lie and Jordan(super)algebras.In the next part, we want to understand the algebras of Moufang-Hopf, a generalization of the universal enveloping algebras of Lie algebras. The final part deals with the Lie algebra of infinite upper triangular matrices. We want to describe its derivations, group of automorphisms and irreducible representations. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FUTORNY, VYACHESLAV; KASHUBA, IRYNA. Structure of parabolically induced modules for affine Kac-Moody algebras. Journal of Algebra, v. 500, n. SI, p. 362-374, APR 15 2018. (14/09310-5, 16/08740-1)

KASHUBA, IRYNA; OVSIENKO, SERGE; SHESTAKOV, IVAN. On the representation type of Jordan basic algebras. ALGEBRA & DISCRETE MATHEMATICS, v. 23, n. 1, p. 47-61, 2017. (16/08740-1)

FUTORNY, VYACHESLAV; KASHUBA, IRYNA. Structure of parabolically induced modules for affine Kac-Moody algebras. Journal of Algebra, v. 500, p. 13-pg., 2018-04-15. (16/08740-1, 14/09310-5)