Representations of Lie Algebras of Vector Fields on Algebraic Varieties

• Grant number: 20/13811-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2021
• End date: April 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Vyacheslav Futorny
• Grantee: Henrique de Oliveira Rocha
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/23690-6 - Structures, representations, and applications of algebraic sistems, AP.TEM
• Associated scholarship(s): 22/00184-3 - Lie Superalgebras of Vector Fields and their Representations, BE.EP.DR

Abstract

This is a PhD research project in Mathematics in the area of Algebra. The main goal is to develop representation theory of Lie algebras of polynomial vector fields on algebraic varieties. Methods of Representation Theory of Lie Algebras, Vertex Algebras and Algebraic Geometry will be used.

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

BOUAZIZ, EMILE; ROCHA, HENRIQUE. Annihilators of AV-modules and differential operators. Journal of Algebra, v. 636, p. 19-pg., 2023-09-27. (22/00184-3, 20/13811-0)

CALIXTO, LUCAS; FUTORNY, VYACHESLAV; ROCHA, HENRIQUE. Harish-Chandra modules for map and affine Lie superalgebras. Israel Journal of Mathematics, v. N/A, p. 30-pg., 2025-05-09. (20/13811-0)

ROCHA, HENRIQUE. Simplicity of the Lie superalgebra of vector fields. COMMUNICATIONS IN ALGEBRA, v. 53, n. 11, p. 5-pg., 2025-05-12. (20/13811-0, 22/00184-3)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

ROCHA, Henrique de Oliveira. Representations of Lie algebras of vector fields on algebraic varieties and supervarieties. 2024. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.