Groups and noncommutative algebra: interactions and applications

Galois Theory, Profinite Groups and applications in quadratic forms.

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Grant number: | 09/52665-0 |

Support type: | Research Projects - Thematic Grants |

Duration: | November 01, 2009 - October 31, 2014 |

Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Algebra |

Principal researcher: | Francisco Cesar Polcino Milies |

Grantee: | Francisco Cesar Polcino Milies |

Home Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |

Principal researchers: | Jairo Zacarias Goncalves ; Mikhailo Dokuchaev |

Associated grant(s): | 13/19544-0 - Partial actions and partial representations,
AV.EXT 12/20425-3 - Twisted partial actions and the Brauer group, AV.BR 12/00878-3 - Some classes of semi-perfect rings, AV.EXT + associated grants - associated grants |

Associated scholarship(s): | 12/20138-4 - About Units of Group Rings and Codes,
BP.PD 12/07610-6 - Partial Schur Multiplier, cohomology and related topics, BP.PD 12/01554-7 - Partial actions and representations, cohomology and globalization, BP.PD |

**Abstract**

We intend to continue the research on the interactions between group theory and non-commutative algebra, and some of its applications. Our group has worked in these directions for quite some time and has already obtained results that are frequently quoted in the literature. Specific subjects to be studied on the period are, among others: the structure of the group of units of a group ring, determining generators of the free complement, in the case of finite abelian groups, and free pairs of generators, in the general case. We shall also study symmetric and skew symmetric elements in a group algebra. 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. Study of codes: cyclic, abelian, metacyclic, etc., using techniques of finite group algebras. (AU)

Scientific publications
(24)

(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)

FERREIRA, VITOR O.;
FORNAROLI, ERICA Z.;
GONCALVES, JAIRO Z.
Free algebras in division rings with an involution.
** Journal of Algebra**,
v. 509,
p. 292-306,
SEP 1 2018.
Web of Science Citations: 1.

GIAMBRUNO, ANTONIO;
MILIES, CESAR POLCINO;
SEHGAL, SUDARSHAN K.
Star-group identities on units of group algebras: The non-torsion case.
** FORUM MATHEMATICUM**,
v. 30,
n. 1,
p. 213-225,
JAN 2018.
Web of Science Citations: 0.

CHALOM, GLADYS;
FERRAZ, RAUL ANTONIO;
GUERREIRO, MARINES.
Minimal ideals in finite abelian group algebras and coding theory.
** SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES**,
v. 10,
n. 2,
p. 321-340,
DEC 2016.
Web of Science Citations: 0.

ABADIE, F.;
DOKUCHAEV, M.;
EXEL, R.;
SIMON, J. J.
MORITA EQUIVALENCE OF PARTIAL GROUP ACTIONS AND GLOBALIZATION.
** Transactions of the American Mathematical Society**,
v. 368,
n. 7,
p. 4957-4992,
JUL 2016.
Web of Science Citations: 3.

BELL, JASON P.;
GONCALVES, JAIRO Z.
Free algebras and free groups in Ore extensions and free group algebras in division rings.
** Journal of Algebra**,
v. 455,
p. 235-250,
JUN 1 2016.
Web of Science Citations: 2.

DOKUCHAEV, M.;
SIMON, J.
ISOMORPHISMS OF PARTIAL GROUP RINGS.
** COMMUNICATIONS IN ALGEBRA**,
v. 44,
n. 2,
p. 680-696,
2016.
Web of Science Citations: 3.

GONCALVES, JAIRO Z.;
PASSMAN, DONALD S.
Free groups in normal subgroups of the multiplicative group of a division ring.
** Journal of Algebra**,
v. 440,
p. 128-144,
OCT 15 2015.
Web of Science Citations: 6.

FERREIRA, VITOR O.;
GONCALVES, JAIRO Z.;
SANCHEZ, JAVIER.
Free symmetric algebras in division rings generated by enveloping algebras of Lie algebras.
** INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION**,
v. 25,
n. 6,
p. 1075-1106,
SEP 2015.
Web of Science Citations: 2.

FERREIRA, VITOR O.;
GONCALVES, JAIRO Z.
Free symmetric and unitary pairs in division rings infinite-dimensional over their centers.
** Israel Journal of Mathematics**,
v. 210,
n. 1,
p. 297-321,
SEP 2015.
Web of Science Citations: 4.

GONCALVES, JAIRO Z.
Constructing free groups in a normal subgroup of the multiplicative group of division rings.
** Journal of Group Theory**,
v. 18,
n. 5,
p. 829-843,
SEP 2015.
Web of Science Citations: 2.

GONCALVES, J. Z.;
PASSMAN, D. S.
EXPLICIT FREE GROUPS IN DIVISION RINGS.
** Proceedings of the American Mathematical Society**,
v. 143,
n. 2,
p. 459-468,
FEB 2015.
Web of Science Citations: 6.

GONCALVES, JAIRO Z.;
LICHTMAN, A. I.
Free subgroups in division rings generated by group rings of soluble groups.
** INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION**,
v. 24,
n. 8,
p. 1127-1140,
DEC 2014.
Web of Science Citations: 2.

GOODAIRE, EDGAR G.;
MILIES, CESAR POLCINO.
Jordan nilpotency in group rings.
** Journal of Group Theory**,
v. 17,
n. 4,
p. 541-557,
JUL 2014.
Web of Science Citations: 1.

GOODAIRE, EDGAR G.;
MILIES, CESAR POLCINO.
ORIENTED GROUP INVOLUTIONS AND ANTICOMMUTATIVITY IN GROUP RINGS.
** COMMUNICATIONS IN ALGEBRA**,
v. 42,
n. 4,
p. 1657-1667,
APR 3 2014.
Web of Science Citations: 0.

FERREIRA, VITOR O.;
MURAKAMI, LUCIA S. I.
RATIONALITY OF THE HILBERT SERIES OF HOPF-INVARIANTS OF FREE ALGEBRAS.
** Proceedings of the American Mathematical Society**,
v. 142,
n. 3,
p. 821-826,
MAR 2014.
Web of Science Citations: 0.

FERRAZ, RAUL ANTONIO;
GUERREIRO, MARINES;
MILIES, CESAR POLCINO.
G-Equivalence in Group Algebras and Minimal Abelian Codes.
** IEEE TRANSACTIONS ON INFORMATION THEORY**,
v. 60,
n. 1,
p. 252-260,
JAN 2014.
Web of Science Citations: 2.

MILIES, CESAR POLCINO;
DE MELO, FERNANDA DINIZ.
On Cyclic and Abelian Codes.
** IEEE TRANSACTIONS ON INFORMATION THEORY**,
v. 59,
n. 11,
p. 7314-7319,
NOV 2013.
Web of Science Citations: 4.

FERREIRA, VITOR O.;
GONCALVES, JAIRO Z.;
SANCHEZ, JAVIER.
Free symmetric group algebras in division rings generated by poly-orderable groups.
** Journal of Algebra**,
v. 392,
p. 69-84,
OCT 15 2013.
Web of Science Citations: 4.

GOODAIRE, EDGAR G.;
MILIES, CESAR POLCINO.
ORIENTED INVOLUTIONS AND SKEW-SYMMETRIC ELEMENTS IN GROUP RINGS.
** JOURNAL OF ALGEBRA AND ITS APPLICATIONS**,
v. 12,
n. 1
FEB 2013.
Web of Science Citations: 1.

GONCALVES, J. Z.;
TENGAN, E.
FREE GROUP ALGEBRAS IN DIVISION RINGS.
** INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION**,
v. 22,
n. 5
AUG 2012.
Web of Science Citations: 4.

CASTILLO GOMEZ, JOHN H.;
MILIES, CESAR POLCINO.
LIE PROPERTIES OF SYMMETRIC ELEMENTS UNDER ORIENTED INVOLUTIONS.
** COMMUNICATIONS IN ALGEBRA**,
v. 40,
n. 12,
p. 4404-4419,
2012.
Web of Science Citations: 4.

GONCALVES, J. Z.;
SHIRVANI, M.
A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION.
** COMMUNICATIONS IN ALGEBRA**,
v. 40,
n. 5,
p. 1704-1723,
2012.
Web of Science Citations: 14.

GONCALVES, J. Z.;
PASSMAN, D. S.
INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS.
** JOURNAL OF ALGEBRA AND ITS APPLICATIONS**,
v. 10,
n. 4,
p. 711-725,
AUG 2011.
Web of Science Citations: 1.

GIAMBRUNO, ANTONIO;
MILIES, CESAR POLCINO;
SEHGAL, SUDARSHAN K.
Star-group identities and groups of units.
** ARCHIV DER MATHEMATIK**,
v. 95,
n. 6,
p. 501-508,
DEC 2010.
Web of Science Citations: 7.

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