Lie semigroups, homotopy, and global extensions of local homomorphisms
For a finite dimensional connected Lie group G with Lie algebra g, we consider a Lie-generating Lie wedge W ⊆ g. If S is a Lie subsemigroup of G with subtangent wedge W we give sufficient conditions for S to be free on small enough local semigroups U ∩ S in the sense that continuous local homomorphisms extend to global ones on S. The constructions involve developing a homotopy theory of U ∩ S-directed paths. We also consider settings where the free construction leads to a simply connected covering of S.
Publication Source (Journal or Book title)
Journal of Lie Theory
Kizil, E., & Lawson, J. (2015). Lie semigroups, homotopy, and global extensions of local homomorphisms. Journal of Lie Theory, 25 (3), 753-774. Retrieved from https://digitalcommons.lsu.edu/mathematics_pubs/583