Title
On a subsemigroup of the universal covering of Lie semigroups
Document Type
Article
Publication Date
12-1-2014
Abstract
Let G be a connected Lie group and S a generating Lie semigroup. An important fact is that generating Lie semigroups admit simply connected covering semigroups. Denote by (formula presented) the simply connected universal covering semigroup of S. In connection with the problem of identifying the semigroup (formula presented) of monotonic homotopy with a certain subsemigroup of the simply connected covering semigroup (formula presented) we consider in this paper the following subsemigroup (formula presented) where Exp: (formula presented) is the lifting to (formula presented) of the exponential mapping exp : (formula presented). We prove that (formula presented) is also simply connected under the assumption that the Lie semigroup S is right reversible. We further comment how this result should be related to the identification problem mentioned above.
Publication Source (Journal or Book title)
Semigroup Forum
First Page
627
Last Page
638
Recommended Citation
Kizil, E., & Lawson, J. (2014). On a subsemigroup of the universal covering of Lie semigroups. Semigroup Forum, 89 (3), 627-638. https://doi.org/10.1007/s00233-014-9597-9