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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 researcher:Ivan Chestakov
Grantee:Ivan Chestakov
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Pesquisadores principais:
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):21/12820-9 - Loops and related algebras, AV.EXT
21/09845-0 - Conformal invariance of the probability density function for passive scalar fields (including arbitrary virus) in 2D turbulence - the proof of Polyakov conjecture., AV.EXT
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):22/00024-6 - Representations of infinite dimensional Lie algebras and theory of vertex algebras, BP.PD
22/00376-0 - Hochschild (co)homology and global dimension, BP.IC
21/13052-5 - Loops and related groups, BP.PD
+ associated scholarships 21/13022-9 - Representations of Lie algebras and superalgebras, BP.PD
21/14493-5 - Hochschild (co)homology, BP.IC
21/12353-1 - Images of polynomials in algebras, BP.IC
20/16595-7 - Polynomial identities and their numerical invariants, BP.MS
21/10214-4 - Two theorems of Gabriel, BP.IC
21/03733-5 - Polynomial identities of matrix algebra with additional structures, BP.PD
20/13811-0 - Representations of Lie Algebras of vector fields on algebraic varieties, BP.DR
20/14281-5 - Representations of twisted affine Lie Superalgebras and their quantizations, BP.PD
20/14313-4 - Cuspidal Representations of Lie Algebras, BP.DR
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
19/23380-0 - Weyl modules and Frobenius-Schur duality, BP.MS
19/24494-9 - Representations of W-algebras, BP.DR
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)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (39)
(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; SCHWARZ, JOAO; SHESTAKOV, IVAN. LD-stability for Goldie rings. Journal of Pure and Applied Algebra, v. 225, n. 11, . (18/23690-6, 18/18146-5)
IUSENKO, KOSTIANTYN; MACQUARRIE, JOHN WILLIAM; QUIRINO, SAMUEL. A Functorial Approach to Gabrielk-quiver Constructions for Coalgebras and Pseudocompact Algebras. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 52, n. 3, p. 697-719, . (18/23690-6, 14/09310-5)
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, . (18/02108-7, 18/23690-6)
MESHKOV, A. G.; SOKOLOV, V. V.. Classification of integrable vector equations of geometric type. JOURNAL OF GEOMETRY AND PHYSICS, v. 149, . (18/23690-6)
KOCHLOUKOVA, DESSISLAVA H.; MENDONCA, LUIS. Weak commutativity for pro-pgroups. MONATSHEFTE FUR MATHEMATIK, v. 194, n. 3, p. 555-575, . (15/22064-6, 18/23690-6)
BIANCHI, ANGELO; CHAMBERLIN, SAMUEL. Weyl modules and Weyl functors for hyper-map algebras. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 20, n. 1, SI, . (15/22040-0, 18/23690-6)
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, . (18/23690-6)
SHESTAKOV, I.; ZAICEV, M.. Eventually non-decreasing codimensions of {*}-identities. ARCHIV DER MATHEMATIK, v. 116, n. 4, . (19/02510-2, 18/23690-6)
SHESTAKOV, IVAN; ZAICEV, MIKHAIL. Codimension growth of simple Jordan superalgebras. Israel Journal of Mathematics, v. 245, n. 2, . (19/02510-2, 18/23690-6)
KOCHLOUKOVA, DESSISLAVA H.. ON THE BIERI-NEUMANN-STREBEL-RENZ Sigma(1)-INVARIANT OF EVEN ARTIN GROUPS. PACIFIC JOURNAL OF MATHEMATICS, v. 312, n. 1, p. 149-169, . (18/23690-6)
GRISHKOV, ALEXANDER; RASSKAZOVA, MARINA; SABININA, LIUDMILA; SALIM, MOHAMED. On Malcev algebras nilpotent by Lie center and corresponding analytic Moufang loops. Journal of Algebra, v. 575, p. 67-77, . (19/24418-0, 18/23690-6, 18/11292-6)
GUIMARAES, ALAN DE ARAUJO; KOSHLUKOV, PLAMEN. Z-graded polynomial identities of the Grassmann algebra. Linear Algebra and its Applications, v. 617, p. 190-214, . (18/23690-6)
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, . (18/23690-6)
FUTORNY, VYACHESLAV. Representations of Lie algebras. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, . (18/23690-6)
DA SILVA MACEDO, DAVID LEVI; KOSHLUKOV, PLAMEN. odimension growth for polynomial identities of representations of Lie algebra. Mathematische Nachrichten, v. 295, n. 2, p. 281-308, . (18/23690-6)
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, . (18/23690-6)
FUTORNY, VYACHESLAV; SCHWARZ, JOAO. Algebras of invariant differential operators. Journal of Algebra, v. 542, p. 215-229, . (18/18146-5, 16/14648-0, 14/25612-1, 18/23690-6)
IOPPOLO, ANTONIO; KOSHLUKOV, PLAMEN; LA MATTINA, DANIELA. Matrix algebras with degenerate traces and trace identities. Journal of Algebra, v. 592, p. 36-63, . (18/17464-3, 18/23690-6)
BEHN, A.; CORREA, IVAN; GUTIERREZ FERNANDEZ, JUAN C.; GARCIA, I, C.. About nilalgebras satisfying (xy)(2) = x(2)y(2). COMMUNICATIONS IN ALGEBRA, v. 49, n. 9, p. 3708-3719, . (18/23690-6)
FUTORNY, VYACHESLAV; GRANTCHAROV, DIMITAR; RAMIREZ, LUIS ENRIQUE. Classification of simple Gelfand-Tsetlin modules of sl(3). BULLETIN OF MATHEMATICAL SCIENCES, v. 11, n. 03, . (18/17955-7, 18/23690-6)
FUTORNY, VYACHESLAV; SCHWARZ, JOAO. Holonomic modules for rings of invariant differential operators. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, v. 31, n. 04, p. 605-622, . (18/18146-5, 18/23690-6)
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, . (18/24089-4, 18/23690-6)
POZHIDAEV, A. P.; SHESTAKOV, I. P.. Simple Right-Symmetric (1,1)-Superalgebras. Algebra and Logic, v. 60, n. 2, . (18/23690-6, 18/05372-7)
KOCHLOUKOVA, DESSISLAVA H.; MARTINEZ-PEREZ, CONCHITA. Generalizations of Weak Commutativity for Lie Algebras. JOURNAL OF LIE THEORY, v. 31, n. 2, p. 469-492, . (18/23690-6)
DINIZ, DIOGO; FIDELIS, CLAUDEMIR; KOSHLUKOV, PLAMEN. GRADED IDENTITIES FOR ALGEBRAS WITH ELEMENTARY GRADINGS OVER AN INFINITE FIELD. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, . (18/23690-6, 19/12498-0)
SHESTAKOV, IVAN; ZHANG, ZERUI. Automorphisms of finitely generated relatively free bicommutative algebras. Journal of Pure and Applied Algebra, v. 225, n. 8, . (19/02095-5, 18/23690-6)
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, . (18/24089-4, 18/23690-6)
KOCHLOUKOVA, DESSISLAVA H.; LEON, ADRIANA JUZGA. Finitely presented metabelian restricted Lie algebras. Journal of Algebra, v. 560, p. 1107-1145, . (18/23690-6)
CHEN, YUQUN; SHESTAKOV, IVAN; ZHANG, ZERUI. Free Lie-admissible algebras and an analogue of the PBW theorem. Journal of Algebra, v. 590, p. 234-253, . (18/23690-6)
SANTOS FILHO, G.; MURAKAMI, L.; SHESTAKOV, I. Locally finite coalgebras and the locally nilpotent radical II. COMMUNICATIONS IN ALGEBRA, v. 49, n. 12, . (18/23690-6)
KOCHLOUKOVA, D. H.; MARTINEZ-PEREZ, C.. Bass-Serre theory for Lie algebras: A homological approach. Journal of Algebra, v. 585, p. 143-175, . (18/23690-6)
MURAKAMI, I, L. S.; PERESI, L. A.; SHESTAKOV, I. P.. A retrospect of the research in nonassociative algebras in IME-USP. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, . (18/23690-6)
FIDELIS, CLAUDEMIR; DINIZ, DIOGO; BERNARDO, LEOMAQUES; KOSHLUKOV, PLAMEN. Graded Identities and Central Polynomials for the Verbally Prime Algebras. ALGEBRAS AND REPRESENTATION THEORY, . (19/12498-0, 18/23690-6)
BIANCHI, ANGELO; CHAMBERLIN, SAMUEL. An integral basis for the universal enveloping algebra of the Onsager algebra. COMMUNICATIONS IN ALGEBRA, . (18/23690-6)
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, . (18/23690-6)
CALIXTO, LUCAS; FUTORNY, VYACHESLAV. Highest weight modules for affine Lie superalgebras. REVISTA MATEMATICA IBEROAMERICANA, v. 37, n. 1, p. 129-160, . (18/23690-6)
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, . (18/23690-6, 18/05372-7)
SHESTAKOV, IVAN; ZHANG, ZERUI. Solvability and nilpotency of Novikov algebras. COMMUNICATIONS IN ALGEBRA, . (19/02095-5, 18/23690-6)
PCHELINTSEV, V, S.; SHASHKOV, V, O.; SHESTAKOV, I. P.. Right alternative bimodules over Cayley algebra and coordinatization theorem. Journal of Algebra, v. 572, p. 111-128, . (17/04846-2, 18/23690-6)

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