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The actions of S ( G ) \\mathcal {S}(G) are shown to be in one-to-one correspondence with the partial actions of G G , both in the case of actions on a set, and that of actions as operators on a Hilbert space. In other words, G G and S ( G ) \\mathcal {S}(G) have the same representation theory. We show that S ( G ) \\mathcal S(G) governs the subsemigroup of all closed linear subspaces of a G G -graded C ∗ {C}^* -algebra, generated by the grading subspaces. In the special case of finite groups, the maximum number of such subspaces is computed. A “partial” version of the group C ∗ { C}^* -algebra of a discrete group is introduced. 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Partial actions of groups and actions of inverse semigroups 论文

Partial actions of groups and actions of inverse semigroups · 作者