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Polar and Ol’shanskii decompositions. (English) Zbl 0786.22012

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.

MSC:

22E15 General properties and structure of real Lie groups
22A15 Structure of topological semigroups
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