Representations of (super)algebras of Jordan type

• Grant number: 16/16445-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: November 01, 2016
• End date: September 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Artem Lopatin
• Grantee: Yury Popov
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 19/23347-2 - Monoidal categorifications of cluster algebras, BE.EP.DR

Abstract

We will describe the irreducible representations of simple finite-dimensional noncommutative Jordan and structurable (super)algebras. We will also settle the question of complete reducibility of bimodules over these (super)algebras and finite-dimensionality of their universal multiplicative enveloping algebras.

Scientific publications

(9)

(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)

GORSHKOV, ILYA; KAYGORODOV, IVAN; POPOV, YURY. Degenerations of Jordan Algebras and ``Marginal{''} Algebras. ALGEBRA COLLOQUIUM, v. 28, n. 02, p. 281-294, JUN 2021. (18/15712-0, 16/16445-0)

KAYGORODOV, IVAN; POPOV, YURY. SPLIT REGULAR HOM-LEIBNIZ COLOR 3-ALGEBRAS. Colloquium Mathematicum, v. 157, n. 2, p. 251-277, 2019. (16/16445-0, 17/15437-6)

POPOV, YURY. Representations of simple noncommutative Jordan superalgebras I. Journal of Algebra, v. 544, p. 329-390, FEB 15 2019. (16/16445-0)

KAYGORODOV, IVAN; POPOV, YURY; VOLKOV, YURY. Degenerations of binary Lie and nilpotent Malcev algebras. COMMUNICATIONS IN ALGEBRA, v. 46, n. 11, p. 4928-4940, 2018. (14/24519-8, 16/16445-0, 14/19521-3)

KAYGORODOV, IVAN; LOPES, SAMUEL A.; POPOV, YURY. Degenerations of nilpotent associative commutative algebras. COMMUNICATIONS IN ALGEBRA, v. 48, n. 4, NOV 2019. (18/15712-0, 16/16445-0)

KAYGORODOV, IVAN; LOPATIN, ARTEM; POPOV, YURY. Jordan algebras admitting derivations with invertible values. COMMUNICATIONS IN ALGEBRA, v. 46, n. 1, p. 69-81, 2018. (14/24519-8, 16/16445-0, 16/00541-0)

BEITES, P. D.; KAYGORODOV, IVAN; POPOV, YURY. Generalized Derivations of Multiplicative n-Ary Hom- Color Algebras. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, v. 42, n. 1, p. 315-335, JAN 2019. (16/16445-0, 14/24519-8)

KAYGORODOV, IVAN; POPOV, YURY; POZHIDAEV, ALEXANDR. The universal conservative superalgebra. COMMUNICATIONS IN ALGEBRA, v. 47, n. 10, MAR 2019. (16/16445-0, 18/09299-2)

KAYGORODOV, IVAN; KHRYPCHENKO, MYKOLA; POPOV, YURY. The algebraic and geometric classification of nilpotent terminal algebras. Journal of Pure and Applied Algebra, v. 225, n. 6, JUN 2021. (18/09299-2, 18/15712-0, 16/16445-0)

Academic Publications

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

POPOV, Yury. Representações de superálgebras não comutativas de Jordan. 2020. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.