Lawson, Jimmie D. Polar and Ol’shanskii decompositions. (English) Zbl 0786.22012 J. Reine Angew. Math. 448, 191-219 (1994). We establish general existence theorems for an important class of Lie semigroups called Ol’shanskij semigroups, which are constructed from an invariant cone in a symmetric Lie algebra in a corresponding Lie group. It is shown that these semigroups admit a polar decomposition which generalizes both the polar decomposition of matrices and the Cartan decomposition in semisimple Lie groups. General contraction semigroups and their relatives are studied within this framework. Reviewer: J.D.Lawson (Baton Rouge) Cited in 1 ReviewCited in 13 Documents MSC: 22E15 General properties and structure of real Lie groups 22A15 Structure of topological semigroups Keywords:existence theorems; Lie semigroups; Ol’shanskij semigroups; invariant cone; polar decomposition; contraction semigroups PDFBibTeX XMLCite \textit{J. D. Lawson}, J. Reine Angew. Math. 448, 191--219 (1994; Zbl 0786.22012) Full Text: DOI Crelle EuDML