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Jordan algebras: representations, homology and geometry

Grant number: 21/14716-4
Support Opportunities:Regular Research Grants
Start date: March 01, 2022
End date: February 29, 2024
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 is a research project in the area of Algebra. The project is divided into three parts. The first part is dedicated to the study of representations of Jordan algebras and superalgebras.The second part of the project concerns the investigation of the free Jordan algebra J(n) with n generators, more exactly the structure of the homogeneous component J(n)d of degree d as GL(d)-module. In particular we have conjecture about the dimension of J(n)d (the problem that is open for n e 3 from the 1960's). The aim of the third part is to study the variety of complex Jordan algebras of dimension n using the techniques of geometric invariant theory. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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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)
BEZERRA, LUAN; CALIXTO, LUCAS; FUTORNY, VYACHESLAV; KASHUBA, IRYNA. Representations of affine Lie superalgebras and their quantization in type A. Journal of Algebra, v. 611, p. 21-pg., . (20/14281-5, 21/14716-4, 18/23690-6)
GUERRINI, MARCELA; KASHUBA, IRYNA; MORALES, OSCAR; DE OLIVEIRA, ANDRE; SANTOS, FERNANDO JUNIOR. Generalized imaginary Verma and Wakimoto modules. Journal of Pure and Applied Algebra, v. 227, n. 7, p. 18-pg., . (21/14716-4)