Algebras matrices and varieties

• Grant number: 14/10352-4
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2014
• End date: July 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Thiago Castilho de Mello
• Grantee: Thiago Castilho de Mello
• Host Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil

Abstract

This research project aims to study subvarieties of varieties of infinite basic rank and of small exponent in characteristic zero. More specifically, we intend to classify such subvarieties modulo asymptotic equivalence and study the identities of their relatively free algebras of finite rank. In another research topic, we aim to study the problem of determining the image of a noncommutative multilinear polynomial on matrix algebras - both in ordinary and graded cases. (AU)

Scientific publications

(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)

GONCALVES FONSECA, LUIS FELIPE; DE MELLO, THIAGO CASTILHO. Degree-inverting involutions on matrix algebras. LINEAR & MULTILINEAR ALGEBRA, v. 66, n. 6, p. 1104-1120, 2018. (14/10352-4, 14/09310-5)

GONCALVES FONSECA, LUIS FELIPE; DE MELLO, THIAGO CASTILHO. Graded polynomial Identities for matrices with the transpose involution over an infinite field. COMMUNICATIONS IN ALGEBRA, v. 46, n. 4, p. 1630-1640, 2018. (14/09310-5, 14/10352-4)

PEREIRA DA SILVA E SILVA, DIOGO DINIZ; DE MELLO, THIAGO CASTILHO. Graded identities of block-triangular matrices. Journal of Algebra, v. 464, p. 246-265, OCT 15 2016. (14/09310-5, 14/10352-4)