1-Algebra of a Locally Compact Groupoid | Zendy

Massoud Amini | Zendy; Alireza Medghalchi | Zendy; Ahmad Shirinkalam | Zendy

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1-Algebra of a Locally Compact Groupoid

Author(s) -

Massoud Amini,

Alireza Medghalchi,

Ahmad Shirinkalam

Publication year - 2011

Publication title -

isrn algebra

Language(s) - English

Resource type - Journals

eISSN - 2090-6293

pISSN - 2090-6285

DOI - 10.5402/2011/856709

Subject(s) - mathematics , locally compact space , locally compact group , pure mathematics , hilbert space , algebra over a field , banach algebra , haar measure , class (philosophy) , invariant (physics) , integrable system , ideal (ethics) , banach space , computer science , philosophy , epistemology , artificial intelligence , mathematical physics

For a locally compact groupoid with a fixed Haar system and quasi-invariant measure ,we introduce the notion of -measurability and construct the space 1 (, , ) of absolutely integrablefunctions on and show that it is a Banach -algebra and a two-sided ideal in the algebra ()of complex Radon measures on . We find correspondences between representations of on Hilbertbundles and certain class of nondegenerate representations of 1 (, , ).

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