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Semigroup actions on operator algebras

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OAS - Operator algebras: subfactors and their applications

We will present a dilation technique from commuting endomorphisms to commuting automophisms on a larger C-algebra such that the corresponding (minimal) Cuntz-Nica-Pimsner algebras are strong Morita equivalent. Hence we can reduce problems on semigroup actions to problems on group actions. Further consequences of our analysis include the association of the ideal structure/nuclearity/exactness of the Nica-Pimsner algebras with minimality-freeness/nuclearity/exactness of the C-dynamics.



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