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Non commutative algebra and applications

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)

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Scientific publications (19)
(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)
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, . (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, . (18/25269-6, 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, . (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, . (12/01554-7, 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, . (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, . (15/09162-9)
SANCHEZ, JAVIER. Free group algebras in division rings with valuation I. Journal of Algebra, v. 531, p. 221-248, . (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, . (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, . (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, . (15/09162-9, 13/11350-2, 15/16726-6, 14/23853-1)
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, . (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, . (12/01554-7, 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, . (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, . (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, . (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, . (15/09162-9, 12/01554-7)
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, . (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, . (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, . (15/09162-9)

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