Lie Semigroups, Homotopy, and Global Extensions of Local Homomorphisms


KIZIL E. , Lawson J.

JOURNAL OF LIE THEORY, vol.25, no.3, pp.753-774, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 3
  • Publication Date: 2015
  • Title of Journal : JOURNAL OF LIE THEORY
  • Page Numbers: pp.753-774

Abstract

For a finite dimensional connected Lie group G with Lie algebra g, we consider a Lie-generating Lie wedge W subset of 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 boolean AND S in the sense that continuous local homomorphisms extend to global ones on S. The constructions involve developing a homotopy theory of U boolean AND S-directed paths. We also consider settings where the free construction leads to a simply connected covering of S.