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Covering Semigroup for invariant systems on Lie Groups

Grant number: 11/17476-2
Support Opportunities:Regular Research Grants
Duration: May 01, 2012 - 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)

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