1Instituto de Ciências Matemáticas, Universidade de São Paulo, Cx. Postal 668 -- CEP 13.560-970, São Carlos -- SP, Brasil 2Dept. of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
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 $S$.
1
Instituto de Ciências Matemáticas, Universidade de São Paulo, Cx. Postal 668 -- CEP 13.560-970, São Carlos -- SP, Brasil
2
Dept. of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
Eyüp Kizil; Jimmie 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/JOLT_2015_25_3_a5/
@article{JOLT_2015_25_3_a5,
author = {Ey\"up Kizil and Jimmie 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/JOLT_2015_25_3_a5/}
}
TY - JOUR
AU - Eyüp Kizil
AU - Jimmie Lawson
TI - Lie Semigroups, Homotopy, and Global Extensions of Local Homomorphisms
JO - Journal of Lie Theory
PY - 2015
SP - 753
EP - 774
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a5/
ID - JOLT_2015_25_3_a5
ER -
%0 Journal Article
%A Eyüp Kizil
%A Jimmie Lawson
%T Lie Semigroups, Homotopy, and Global Extensions of Local Homomorphisms
%J Journal of Lie Theory
%D 2015
%P 753-774
%V 25
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a5/
%F JOLT_2015_25_3_a5
