Separability of compact quantum groups

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In the theory of compact quantum groups due Woronowicz, we assume usually that the C*-algebra of the compact quantum group is separable. Is the assumption essential in the theory? Will it eventually make sense to develop the theory of nonseparable compact quantum groups? What has gone wrong?






oa.operator-algebras qa.quantum-algebra quantum-groups noncommutative-geometry







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    Carlo has given a reference to a general framework by van Daele, but it is worth noting that the reduced $rm C^*$-algebra of any discrete group has always been recognized as an example of a compact quantum group (in fact, a compact Kac algebra) and this will be non-separable as soon as the discrete group is uncountable
    – Yemon Choi
    3 hours ago














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In the theory of compact quantum groups due Woronowicz, we assume usually that the C*-algebra of the compact quantum group is separable. Is the assumption essential in the theory? Will it eventually make sense to develop the theory of nonseparable compact quantum groups? What has gone wrong?






oa.operator-algebras qa.quantum-algebra quantum-groups noncommutative-geometry







share|cite|improve this question







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Marie Anderlecht is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • 3




    Carlo has given a reference to a general framework by van Daele, but it is worth noting that the reduced $rm C^*$-algebra of any discrete group has always been recognized as an example of a compact quantum group (in fact, a compact Kac algebra) and this will be non-separable as soon as the discrete group is uncountable
    – Yemon Choi
    3 hours ago












up vote
4
down vote

favorite









up vote
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down vote

favorite











In the theory of compact quantum groups due Woronowicz, we assume usually that the C*-algebra of the compact quantum group is separable. Is the assumption essential in the theory? Will it eventually make sense to develop the theory of nonseparable compact quantum groups? What has gone wrong?






oa.operator-algebras qa.quantum-algebra quantum-groups noncommutative-geometry







share|cite|improve this question







New contributor




Marie Anderlecht is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











In the theory of compact quantum groups due Woronowicz, we assume usually that the C*-algebra of the compact quantum group is separable. Is the assumption essential in the theory? Will it eventually make sense to develop the theory of nonseparable compact quantum groups? What has gone wrong?






oa.operator-algebras qa.quantum-algebra quantum-groups noncommutative-geometry




oa.operator-algebras qa.quantum-algebra quantum-groups noncommutative-geometry






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Marie Anderlecht is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











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  • 3




    Carlo has given a reference to a general framework by van Daele, but it is worth noting that the reduced $rm C^*$-algebra of any discrete group has always been recognized as an example of a compact quantum group (in fact, a compact Kac algebra) and this will be non-separable as soon as the discrete group is uncountable
    – Yemon Choi
    3 hours ago












  • 3




    Carlo has given a reference to a general framework by van Daele, but it is worth noting that the reduced $rm C^*$-algebra of any discrete group has always been recognized as an example of a compact quantum group (in fact, a compact Kac algebra) and this will be non-separable as soon as the discrete group is uncountable
    – Yemon Choi
    3 hours ago







3




3




Carlo has given a reference to a general framework by van Daele, but it is worth noting that the reduced $rm C^*$-algebra of any discrete group has always been recognized as an example of a compact quantum group (in fact, a compact Kac algebra) and this will be non-separable as soon as the discrete group is uncountable
– Yemon Choi
3 hours ago




Carlo has given a reference to a general framework by van Daele, but it is worth noting that the reduced $rm C^*$-algebra of any discrete group has always been recognized as an example of a compact quantum group (in fact, a compact Kac algebra) and this will be non-separable as soon as the discrete group is uncountable
– Yemon Choi
3 hours ago










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A Haar measure on a compact quantum group without requiring separability was constructed in The Haar measure on a compact quantum group (1995).






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    A Haar measure on a compact quantum group without requiring separability was constructed in The Haar measure on a compact quantum group (1995).






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      A Haar measure on a compact quantum group without requiring separability was constructed in The Haar measure on a compact quantum group (1995).






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        A Haar measure on a compact quantum group without requiring separability was constructed in The Haar measure on a compact quantum group (1995).






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        A Haar measure on a compact quantum group without requiring separability was constructed in The Haar measure on a compact quantum group (1995).







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        answered 3 hours ago









        Carlo Beenakker

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