Lie Semigroups, Homotopy, and Global Extensions of Local Homomorphisms
Journal of Lie theory, Tome 25 (2015) no. 3, pp. 753-774
\def\g{{\frak g}} For a finite dimensional connected Lie group $G$ with Lie algebra $\g$, we consider a Lie-generating 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 $S$.
Classification :
22A15, 22E15
Mots-clés : Lie semigroup, local semigroup, Lie wedge, Lie group, homotopic paths, covering semigroups
Mots-clés : Lie semigroup, local semigroup, Lie wedge, Lie group, homotopic paths, covering semigroups
@article{JLT_2015_25_3_JLT_2015_25_3_a5,
author = {E. Kizil and J. Lawson},
title = {Lie {Semigroups,} {Homotopy,} and {Global} {Extensions} of {Local} {Homomorphisms}},
journal = {Journal of Lie theory},
pages = {753--774},
year = {2015},
volume = {25},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_3_JLT_2015_25_3_a5/}
}
E. Kizil; J. Lawson. Lie Semigroups, Homotopy, and Global Extensions of Local Homomorphisms. Journal of Lie theory, Tome 25 (2015) no. 3, pp. 753-774. http://geodesic.mathdoc.fr/item/JLT_2015_25_3_JLT_2015_25_3_a5/