Covering Semigroup for invariant systems on Lie Groups

• Grant number: 11/17476-2
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2012
• End date: July 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Eyüp Kizil
• Grantee: Eyüp Kizil
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Let G be a Lie group with identity eG and £ a cone in the Lie algebra g of G. We think of g as the set of left invariant vector fields on G and assume furthermore that it satisfies the Lie algebra rank condition. We use a general formalism developed by Sussmann to obtain an algebraic structure on the covering space “(£,x), xG, recently presented by Colonius-Kizil-San Martin. This formalism provides a Lie group of exponentials of Lie series and a subsemigroup S that parametrizes the space of controls by means of Chen series. The main purpose of the project is to obtain the monotonic covering “(£,x) as appropriate quotients of the above semigroup S through congruence relations on semigroups. (AU)