Algebraic structures of the baric algebras, RA loops and linear codes

• Grant number: 12/10378-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2012
• End date: August 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Henrique Guzzo Junior
• Grantee: Rodrigo Lucas Rodrigues
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 10/50347-9 - Algebras, representations e applications, AP.TEM

Abstract

The focus of this project is the study of rings and algebras that are not necessarily associative. The inicial goal of the candidate is to finish solving some problems of his PhD which are in advanced development, such as determining the baric composition algebras, the b-radical of a group algebra and study the question of the anticommutativity of skew-symmetric elements of an RA loop under oriented involutions.A second purpose, related to the study of the algebraic structures of a b-algebra, it is to determine nilpotence and solvability conditions to some particular algebras, such as the power-associative and the alternative, and to prove our conjecture about a type of Wedderburn theorem for alternative b-algebras. A third line is to use tecniques of group algebras and representations to extend some results on optimal linear codes in the error correcting codes theory, work that will be developed together with experts Dr. Francisco Cesar Polcino Milies and Dra. Consuelo Martinez Lopez. Finally, together with the expert Dr. Joao Carlos Motta Ferreira, to research about a subject that has been studied for associative rings, which is to determine when a multiplicative derivations defined on either power-associative or alternative rings is aditive.

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)

RODRIGUES, R. L.; GUZZO, JR., H.; FERREIRA, J. C. M.. When is a Multiplicative Derivation Additive in Alternative Rings?. COMMUNICATIONS IN ALGEBRA, v. 44, n. 6, p. 2561-2566, 2016. (12/10378-8, 10/50347-9)