
Journal of Lie Theory 25 (2015), No. 3, 753774 Copyright Heldermann Verlag 2015 Lie Semigroups, Homotopy, and Global Extensions of Local Homomorphisms Eyüp Kizil Instituto de Ciências Matemáticas, Universidade de São Paulo, Cx. Postal 668  CEP 13.560970, São Carlos  SP, Brasil kizil@icmc.usp.br Jimmie Lawson Dept. of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A. lawson@math.lsu.edu [Abstractpdf] \def\g{{\frak g}} For a finite dimensional connected Lie group $G$ with Lie algebra $\g$, we consider a Liegenerating Lie wedge ${\bf W}\subseteq \g$. If $S$ is a Lie subsemigroup of $G$ with subtangent wedge ${\bf W}$ we give sufficient conditions for $S$ to be free on small enough local semigroups $U\cap S$ in the sense that continuous local homomorphisms extend to global ones on $S$. The constructions involve developing a homotopy theory of $U\cap S$directed paths. We also consider settings where the free construction leads to a simply connected covering of $S$. Keywords: Lie semigroup, local semigroup, Lie wedge, Lie group, homotopic paths, covering semigroups. MSC: 22A15, 22E15 [ Fulltextpdf (349 KB)] for subscribers only. 