Advanced search
Start date
Betweenand

Structures, representations, and applications of algebraic systems

Grant number: 18/23690-6
Support type:Research Projects - Thematic Grants
Duration: July 01, 2019 - June 30, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Ivan Chestakov
Grantee:Ivan Chestakov
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Co-Principal Investigators:Adriano Adrega de Moura ; Alexandre Grichkov ; Dessislava Hristova Kochloukova ; Eduardo Do Nascimento Marcos ; Plamen Emilov Kochloukov ; Vyacheslav Futorny
Assoc. researchers:Alexandr Kornev ; Angelo Calil Bianchi ; Artem Lopatin ; Dimas José Gonçalves ; Fernanda de Andrade Pereira ; Henrique Guzzo Junior ; Iryna Kashuba ; Juan Carlos Gutiérrez Fernández ; Kostiantyn Iusenko ; Lucia Satie Ikemoto Murakami ; Lucio Centrone ; Luis Enrique Ramírez ; Renato Alessandro Martins ; Thiago Castilho de Mello ; Vladimir Sokolov
Associated grant(s):19/23251-5 - Representations of Lie algebras of vector fields on algebraic varieties, AP.R SPRINT
19/24418-0 - Restricted Burnside problem, reductive Moufang Loops and their tangent algebras, AV.EXT
Associated scholarship(s):20/10831-0 - Group Theory and Bezout's theorem for curves, BP.IC
20/11159-4 - Theory of Groups and Gabriel's theorem, BP.IC
19/12498-0 - Graded polynomial identities and identity with trace, and invariant theory, BP.PD
+ associated scholarships 19/24494-9 - Representations of W-algebras, BP.DR
19/23380-0 - Weyl modules and Frobenius-Schur duality, BP.MS
19/22813-0 - Algebras with polynomial identities, BP.IC
19/17085-5 - Groups, representations, and applications, BP.IC
19/17092-1 - Groups, fields, Galois theory, and applications, BP.IC
19/16994-1 - Algebras that are sums of two PI subalgebras, BP.DR - associated scholarships

Abstract

Most of the project will be dedicated to Lie and Jordan algebras and superalgebras and their representations. In addition, Malcev and alternative algebras and superalgebras will be considered, Moufang loops and various generalizations and applications of above. Algebraic systems related to integrable systems of differential equations will be considered. Homological methods will be applied in the theory of representations and finely presentable algebraic structures. The lines of the research project focus on the following themes: representations of Lie algebras and superalgebras; structural questions for representations of related Kac-Moody algebras and their generalizations; non-associative algebras, their applications and generalizations; representations of Lie and Jordan superalgebras, application of Tits-Kantor-Koecher construction free Jordan algebra; combinatorial theory of algebras; theory of loops, their relations and applications; integrable systems and non-associative structures; representations of algebras: homological and geometric methods; finitely presentable and homological type FP-m structures. (AU)

Scientific publications (14)
(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)
BONDARENKO, VITALIJ M.; FUTORNY, VYACHESLAV; PETRAVCHUK, ANATOLII P.; SERGEICHUK, VLADIMIR V. Pairs of commuting nilpotent operators with one-dimensional intersection of kernels and matrices commuting with a Weyr matrix. Linear Algebra and its Applications, v. 612, p. 188-205, MAR 1 2021. Web of Science Citations: 0.
POZHIDAEV, A. P.; SHESTAKOV, I. P. ON THE RIGHT-SYMMETRIC ALGEBRAS WITH A UNITAL MATRIX SUBALGEBRA. SIBERIAN MATHEMATICAL JOURNAL, v. 62, n. 1, p. 138-147, JAN 2021. Web of Science Citations: 0.
SHESTAKOV, I.; ZAICEV, M. Eventually non-decreasing codimensions of {*}-identities. ARCHIV DER MATHEMATIK, JAN 2021. Web of Science Citations: 0.
CALIXTO, LUCAS; FUTORNY, VYACHESLAV. Highest weight modules for affine Lie superalgebras. REVISTA MATEMATICA IBEROAMERICANA, v. 37, n. 1, p. 129-160, 2021. Web of Science Citations: 0.
DA SILVA MACEDO, DAVID LEVI; KOSHLUKOV, PLAMEN. CODIMENSION GROWTH FOR WEAK POLYNOMIAL IDENTITIES, AND NON-INTEGRALITY OF THE PI EXPONENT. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 63, n. 4, p. 929-949, NOV 2020. Web of Science Citations: 0.
CENTRONE, LUCIO; GONCALVES, DIMAS JOSE; SILVA, DALTON COUTO. Identities and central polynomials with involution for the Grassmann algebra. Journal of Algebra, v. 560, p. 219-240, OCT 15 2020. Web of Science Citations: 0.
KOCHLOUKOVA, DESSISLAVA H.; LEON, ADRIANA JUZGA. Finitely presented metabelian restricted Lie algebras. Journal of Algebra, v. 560, p. 1107-1145, OCT 15 2020. Web of Science Citations: 0.
GONCALVES, DIMAS JOSE; RIVA, EVANDRO. Graded polynomial identities for the upper triangular matrix algebra over a finite field. Journal of Algebra, v. 559, p. 625-645, OCT 1 2020. Web of Science Citations: 0.
MACEDO FERREIRA, BRUNO LEONARDO; GUZZO JR, HENRIQUE; FERREIRA, RUTH NASCIMENTO. An Approach Between the Multiplicative and Additive Structure of a Jordan Ring. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, JUL 2020. Web of Science Citations: 0.
SHESTAKOV, IVAN; ZHANG, ZERUI. Solvability and nilpotency of Novikov algebras. COMMUNICATIONS IN ALGEBRA, JUL 2020. Web of Science Citations: 0.
CRODE, SIDNEY DALE; SHESTAKOV, IVAN P. Locally nilpotent derivations and automorphisms of free associative algebra with two generators. COMMUNICATIONS IN ALGEBRA, v. 48, n. 7 MAR 2020. Web of Science Citations: 0.
MESHKOV, A. G.; SOKOLOV, V. V. Classification of integrable vector equations of geometric type. JOURNAL OF GEOMETRY AND PHYSICS, v. 149, MAR 2020. Web of Science Citations: 0.
CAALIM, V, JONATHAN; FUTORNY, VYACHESLAV; SERGEICHUK, VLADIMIR V.; TANAKA, YU-ICHI. Isometric and selfadjoint operators on a vector space with nondegenerate diagonalizable form. Linear Algebra and its Applications, v. 587, p. 92-110, FEB 15 2020. Web of Science Citations: 0.
FUTORNY, VYACHESLAV; SCHWARZ, JOAO. Algebras of invariant differential operators. Journal of Algebra, v. 542, p. 215-229, JAN 15 2020. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.