Algebraic and analytic loops and relation algebras

• Grant number: 05/00666-2
• Support Opportunities: Regular Research Grants
• Start date: October 01, 2005
• End date: September 30, 2007
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Alexandre Grichkov
• Grantee: Alexandre Grichkov
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The main object of this reseach is to develop some analog of Lie theory and algebraic group theory for loops Moufang, diassociative and Bol loops. For this we will use the theory of Lie Groups and algebraic loops with triality, theory of Lie algebras with triality and theory of alternative algebras. As a result we hope to get some criteria for Malcev algebras to be algebraic, to calculate order of commutative free Moufang loops, to construct the new diassociative loops using algebraic diassociative loops. The new simple Lie algebras will be constructed. I want to submit four articles with results of this reseach. (AU)