Non commutative algebra and applications

• Grant number: 15/09162-9
• Support Opportunities: Research Projects - Thematic Grants
• Start date: August 01, 2015
• End date: July 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Francisco Cesar Polcino Milies
• Grantee: Francisco Cesar Polcino Milies
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Pesquisadores principais: Jairo Zacarias Goncalves ; Mikhailo Dokuchaev
• Associated research grant(s): 18/25269-6 - Algebras with polynomial identities, AV.EXT; 18/14122-4 - A mathematical and historical reconsideration of the Lineale Ausdehnungslehre (1944) of Herman Günther Grassmann, AV.EXT; 17/23242-0 - From graded algebras to crossed products, AV.EXT; + associated grants 17/06008-4 - Mathematical Congress of the Americas 2017, AR.EXT; 15/21491-8 - Partial actions, subshifts and related algebras, AV.BR; 15/16726-6 - Tiled orders, exponent matrixes, units in rings and related topics, AV.EXT - associated grants
• Associated scholarship(s): 18/06538-6 - Leavitt path algebras, Steinberg algebras and partial actions, BP.PD; 17/06800-0 - Graded division rings, BP.IC; 15/12139-9 - Schur multiplier and partial actions, BP.PD; 13/11350-2 - Tiled orders, partial actions and homological aspects, BP.PD

Abstract

We intend to continue the research on non commutative algebra. In particular, we wish to study the interactions between Group theory and the Theory of Rings and Algebras, as well as some of its applications, especially, to partial actions of groups on rings and to the Theory of Error-correcting Codes. Our group has worked on these directions for quite some time in the past and has already obtained results that are frequently quoted in the literature. Specific subjects to be studied in the period are, among others:* The structure of group algebras, considered as rings with involution and the group of units of a group ring.* The structure of the group of units of a division ring and the existence of free pairs of special type.* Study of globalization of partial actions, generalized crossed products, isomorphism of partial group algebras, partial actions and co-actions of Hopf algebras, partial projective representations and co-homology based on partial actions.* The study of error-correcting codes, defined from groups. In particular, we expect to study the relations among different classes of codes - cyclic, abelian, metacyclic, etc. - using techniques of finite group algebras. (AU)

Scientific publications

(27)

(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)

FERRAZ, RAUL ANTONIO; FERREIRA, RUTH NASCIMENTO. One-weight codes in some classes of group rings. APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, NOV 2020. (15/09162-9)

SANCHEZ, JAVIER. Obtaining free group algebras in division rings generated by group graded rings. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 17, n. 10, OCT 2018. (15/09162-9)

DOKUCHAEV, MIKHAILO; KHRYPCHENKO, MYKOLA. Partial cohomology of groups and extensions of semilattices of abelian groups. Journal of Pure and Applied Algebra, v. 222, n. 10, p. 2897-2930, OCT 2018. (12/01554-7, 15/09162-9)

DOKUCHAEV, MIKHAILO; KIRICHENKO, VLADIMIR; KUDRYAVTSEVA, GANNA; PLAKHOTNYK, MAKAR. The max-plus algebra of exponent matrices of tiled orders. Journal of Algebra, v. 490, p. 1-20, NOV 15 2017. (15/09162-9, 13/11350-2, 15/16726-6, 14/23853-1)

DOKUCHAEV, MIKHAILO; KHRYPCHENKO, MYKOLA; JACOBO SIMON, JUAN. Globalization of group cohomology in the sense of Alvares-Alves-Redondo. Journal of Algebra, v. 546, p. 604-640, MAR 15 2020. (15/09162-9)

SANCHEZ, JAVIER. Free group algebras in division rings with valuation I. Journal of Algebra, v. 531, p. 221-248, AUG 1 2019. (15/09162-9)

GONCALVES, JAIRO Z.. Free pairs of symmetric and unitary units in normal subgroups of a division ring. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 16, n. 6, JUN 2017. (15/09162-9)

GIAMBRUNO, ANTONIO; MILIES, CESAR POLCINO; ZAICEV, MIKHAIL. A characterization of fundamental algebras through S-n-characters. Journal of Algebra, v. 541, p. 51-60, JAN 1 2020. (15/09162-9)

DOKUCHAEV, MIKHAILO; KHRYPCHENKO, MYKOLA; KUDRYAVTSEVA, GANNA. Partial actions and proper extensions of two-sided restriction semigroups. Journal of Pure and Applied Algebra, v. 225, n. 9, SEP 2021. (15/09162-9)

GIAMBRUNO, A.; LA MATTINA, D.; MILIES, C. POLCINO. UNDERSTANDING STAR-FUNDAMENTAL ALGEBRAS. Proceedings of the American Mathematical Society, v. 149, n. 8, p. 3221-3233, AUG 2021. (18/25269-6, 15/09162-9)

FERREIRA, VITOR O.; GONCALVES, JAIRO Z.; SANCHEZ, JAVIER. Free Symmetric and Unitary Pairs in the Field of Fractions of Torsion-Free Nilpotent Group Algebras. ALGEBRAS AND REPRESENTATION THEORY, v. 23, n. 3, p. 605-619, JUN 2020. (15/09162-9)

FEHLBERG JUNIOR, RENATO; SANCHEZ, JAVIER. On free subalgebras of varieties. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 65, n. 1, p. 13-pg., 2022-02-01. (15/09162-9)

DUARTE, A.; PEREIRA, A.; MILIES, C. POLCINO. Nilpotent group codes. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. N/A, p. 14-pg., 2022-12-13. (15/09162-9)

GONCALVES, JAIRO Z.. Free symmetric pairs in the field of fractions of enveloping Lie algebras with involution. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. N/A, p. 13-pg., 2022-04-15. (15/09162-9)

FERRAZ, RAUL ANTONIO; FERREIRA, RUTH NASCIMENTO. One-weight codes in some classes of group rings. APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, v. 32, n. 3, p. 11-pg., 2020-11-20. (15/09162-9)

ASSUENA, SAMIR; MILIES, CESAR POLCINO; LEROY, A; LOMP, C; LOPEZPERMOUTH, S; OGGIER, F. Good codes from metacyclic groups. RINGS, MODULES AND CODES, v. 727, p. 9-pg., 2019-01-01. (15/09162-9)

GIAMBRUNO, ANTONIO; LA MATTINA, DANIELA; MILIES, CESAR POLCINO. STAR-FUNDAMENTAL ALGEBRAS: POLYNOMIAL IDENTITIES AND ASYMPTOTICS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 373, n. 11, p. 7869-7899, NOV 2020. (15/09162-9)

GONCALVES, JAIRO Z.. Free subgroups in k(x(1), ... , x(n))(X; sigma) and k(x, y)(X; sigma). FORUM MATHEMATICUM, v. 31, n. 3, p. 769-777, MAY 2019. (15/09162-9)

DOKUCHAEV, MIKHAILO; KHRYPCHENKO, MYKOLA. Twisted partial actions and extensions of semilattices of groups by groups. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, v. 27, n. 7, p. 887-933, NOV 2017. (12/01554-7, 15/09162-9)

SILVA, ANDERSON; MILIES, C. POLCINO. CYCLIC CODES OF LENGTH 2p(n) OVER FINITE CHAIN RINGS. Advances in Mathematics of Communications, v. 14, n. 2, p. 233-245, MAY 2020. (15/09162-9)

SANCHEZ, JAVIER. Free Group Algebras in Division Rings with Valuation II. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, v. 72, n. 6, p. 1463-1504, DEC 2020. (15/09162-9)

GONCALVES, JAIRO Z.. Free groups in a normal subgroup of the field of fractions of a skew polynomial ring. COMMUNICATIONS IN ALGEBRA, v. 45, n. 12, p. 5193-5201, 2017. (15/09162-9)

DOKUCHAEV, MIKHAILO; KHRYPCHENKO, MYKOLA; MAKUTA, MAYUMI. The third partial cohomology group and existence of extensions of semilattices of groups by groups. FORUM MATHEMATICUM, v. 32, n. 5, p. 1297-1313, SEP 2020. (15/09162-9)

DOKUCHAEV, MIKHAILO; KHRYPCHENKO, MYKOLA; MAKUTA, MAYUMI. Inverse semigroup cohomology and crossed module extensions of semilattices of groups by inverse semigroups. Journal of Algebra, v. 593, p. 57-pg., 2022-03-01. (15/09162-9)

DUARTE, A.; PEREIRA, A.; MILIES, C. POLCINO. Crossed product codes. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. N/A, p. 12-pg., 2023-10-04. (15/09162-9)

DOKUCHAEV, MIKHAILO; KHRYPCHENKO, MYKOLA; JACOBO SIMON, JUAN. GLOBALIZATION OF PARTIAL COHOMOLOGY OF GROUPS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 374, n. 3, p. 1863-1898, MAR 2021. (15/09162-9, 12/01554-7)

DOKUCHAEV, MIKHAILO; KHRYPCHENKO, MYKOLA. Partial cohomology of groups (vol 427, pg 142, 2015). Journal of Algebra, v. 506, p. 5-pg., 2018-07-15. (15/09162-9, 12/01554-7)