On Lie semigroup analogues of parabolic Lie groups (Q938289)

Motivated by a desire to find a semigroup version of the notion of a parabolic subgroup of a semisimple Lie group, the authors study in this paper closed subsemigroups \(S\) that contain a nilpotent factor \(N\) of an Iwasawa decomposition \(G=KAN\) of a semisimple Lie group \(G\) with finite center. The main result of the paper provides a detailed description and a complete classification of all Lie wedges \(L(S)\) in the Lie algebra \(L(G)\) of \(G\) that are the tangent objects for such semigroups \(S\). In particular, the wedges that arise are what the authors call edge-root wedges, wedges \(W\) with \(\mathfrak{n}\subseteq W\) and \(\mathfrak{k}\cap W\subseteq H(W)\) \((=W\cap-W)\).