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Graded identities in Lie Algebras

Grant number: 07/00447-4
Support Opportunities:Scholarships in Brazil - Doctorate
Start date: August 01, 2007
End date: March 31, 2009
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Plamen Emilov Kochloukov
Grantee:Diogo Diniz Pereira da Silva e Silva
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

We shall study graded identities in Lie algebras and other nonassociative algebras. First we shall study the n-graded identities for the Lie algebra of the n x n traceless matrices over a field K. We shall study the graded identities for the Cayley-Dickson algebra as well, equipped with all possible gradings by finite groups. Having finished this research we shall work with graded identities in other classes of nonassociative algebras. The student is now at his last semester of the master program in Mathematics. He is doing one course for PhD students in summer program, and will be doing two more courses during the first term of 2007. All the three subjects are basic courses for the qualification exam required by our PhD program. Our plans are that he takes this exam in July 2007, before formally entering the program. His master thesis defense is scheduled for July 2007. We observe that the student has excellent marks in all master courses: all his marks are A and in most of the courses his final score was 10.00.

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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)
KOSHLUKOV, PLAMEN; SILVA, DIOGO DINIZ P. S.. 2-Graded polynomial identities for the Jordan algebra of the symmetric matrices of order two. Journal of Algebra, v. 327, n. 1, p. 236-250, . (05/60337-2, 07/00447-4)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
SILVA, Diogo Diniz Pereira da Silva e. Granded identities in non associative algebras. 2010. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP) Campinas, SP.