Abstract
Techniques are developed to study the regular representation and $\sigma$-regular representations of measure groupoids. Convolution, involution, a modular Hilbert algebra, and local and global versions of the regular representation are defined. The associated von Neumann algebras, each uniquely determined by the groupoid and the cocycle $\sigma$, provide a generalization of the group-measure space construction. When the groupoid is principal and ergodic, these algebras are factors. Necessary and sufficient conditions for the $\sigma$-regular representations of a principal ergodic groupoid to be of type I, II, or III are given, as well as a description of the flow of weights; these are independent of $\sigma$. To treat nonergodic groupoids, an ergodic decomposition theorem is provided.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
