Semidirect Product of Groupoids, Its Representations and Random Operators

Details Semidirect Product of Groupoids, Its Representations and Random Operators Semidirect Product of Groupoids, Its Representations and Random Operators

2011-07-09

arxiv.org/abs/1107.1775v1

Physics

Mathematical Physics

13 LaTeX pages

Scientific paper

One of pressing problems in mathematical physics is to find a generalized Poincar\'e symmetry that could be applied to nonflat space-times. As a step in this direction we define the semidirect product of groupoids $\Gamma_0 \rtimes \Gamma_1$ and investigate its properties. We also define the crossed product of a bundle of algebras with the groupoid $\Gamma_1$ and prove that it is isomorphic to the convolutive algebra of the groupoid $\Gamma_0 \rtimes \Gamma_1$. We show that families of unitary representations of semidirect product groupoids in a bundle of Hilbert spaces are random operators. An important example is the Poincar\'e groupoid defined as the semidirect product of the subgroupoid of generalized Lorentz transformations and the subgroupoid of generalized translations.

Affiliated with

Also associated with

No associations

Rating

Semidirect Product of Groupoids, Its Representations and Random Operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Semidirect Product of Groupoids, Its Representations and Random Operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Semidirect Product of Groupoids, Its Representations and Random Operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-674963