Abstract
This paper studies connected components of open subsemigroups of non-compact semi-simple Lie groups by using control sets in the flag manifolds and their coverings. The concept of recurrent component is introduced and a method is given by which their number can be computed. It is shown that the union of all recurrent components is a semigroup. The idea of mid-reversibility comes up to show that an open semigroup has just one semigroup component if the identity belongs to its closure. A necessary and sufficient condition for mid-reversibility is proved showing that e.g. in a complex group any open semigroup is mid-reversible.
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do Rocio, O., San Martin, L. Connected Components of Open Semigroups in Semi-Simple Lie Groups. Semigroup Forum 69, 1–29 (2004). https://doi.org/10.1007/s00233-004-0105-5
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DOI: https://doi.org/10.1007/s00233-004-0105-5