PlanetPhysics/L Compact Quantum Groups

\newcommand{\sqdiagram}[9]{Failed to parse (unknown function "\diagram"): {\displaystyle \diagram #1 \rto^{#2} \dto_{#4}& \eqno{\mbox{#9}}} }

Definition 0.1

A locally compact quantum group defined as in ref. [1] is a quadruple , where is either a - or a - algebra equipped with a co-associative comultiplication and two faithful semi-finite normal weights, and - right and -left Haar measures.


  1. An ordinary unimodular group with Haar measure :

, , where .

  1. A = \L (G) is the von Neumann algebra generated by left-translations or by left convolutions with continuous functions , where , and is the unit of .

All SourcesEdit



  1. 1.0 1.1 Leonid Vainerman. 2003.Locally Compact Quantum Groups and Groupoids: Proceedings of the Meeting of Theoretical Physicists and Mathematicians, Strasbourg, February 21-23, 2002 Series in Mathematics and Theoretical Physics , 2 , Series ed. V. Turaev., Walter de Gruyter Gmbh et Co: Berlin.