Journal of Lie Theory

no. 3
Lie Semigroups, Homotopy, and Global Extensions of Local Homomorphisms
Journal of Lie Theory, Volume 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 $S$.
DOI: 10.5802/jolt.858
Classification: 22A15, 22E15
Keywords: Lie semigroup, local semigroup, Lie wedge, Lie group, homotopic paths, covering semigroups 
@article{JOLT_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},
     doi = {10.5802/jolt.858},
     zbl = {1337.22002},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.858/}
}
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%0 Journal Article
%A E. Kizil
%A J. Lawson
%T Lie Semigroups, Homotopy, and Global Extensions of Local Homomorphisms
%J Journal of Lie Theory
%D 2015
%P 753-774
%V 25
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%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.858/
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E. Kizil; J. Lawson. Lie Semigroups, Homotopy, and Global Extensions of Local Homomorphisms. Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 753-774. doi: 10.5802/jolt.858

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