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The Lvov-Kaplansky conjecture

Grant number: 16/09496-7
Support Opportunities:Scholarships in Brazil - Master
Effective date (Start): September 01, 2016
Effective date (End): January 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Thiago Castilho de Mello
Grantee:Pedro Souza Fagundes
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
Associated research grant:14/09310-5 - Algebraic structures and their representations, AP.TEM
Associated scholarship(s):17/16864-5 - Images of polynomials on algebras, BE.EP.MS


The Lvov-Kaplansky conjecture states that the image of the matrix algebra $M_n(F)$, by a multilinear polynomial is a vector subspace of $M_n(F)$. There are many results in the literature, specially in the last 4 years, with partial answers for such problem and also for generalizations for some non-associative matrix algebras. The aim of this project is a detailed study of such results, analizing the differences of each case and highlighting the difficulties to generalize these results and to obtain a solution for the conjecture. (AU)

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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)
FAGUNDES, PEDRO SOUZA; DE MELLO, THIAGO CASTILHO; DOS SANTOS, PEDRO HENRIQUE DA SILVA. On the Mesyan conjecture. TURKISH JOURNAL OF MATHEMATICS, v. 46, n. 5, p. 16-pg., . (16/09496-7, 19/16994-1, 18/23690-6)
FAGUNDES, PEDRO S.. The images of multilinear polynomials on strictly upper triangular matrices. Linear Algebra and its Applications, v. 563, p. 287-301, . (16/09496-7, 17/16864-5)

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