On a subsemigroup of the universal covering of Lie semigroups
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)
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