About: Compact quantum group

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In mathematics, a compact quantum group is an abstract structure on a unital separable C*-algebra axiomatized from those that exist on the commutative C*-algebra of "continuous complex-valued functions" on a compact quantum group.

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rdfs:label	Compact quantum group (en)
rdfs:comment	In mathematics, a compact quantum group is an abstract structure on a unital separable C-algebra axiomatized from those that exist on the commutative C-algebra of "continuous complex-valued functions" on a compact quantum group. (en)
dcterms:subject	Quantum groups C*-algebras Hopf algebras
Wikipage page ID	3852696 (xsd:integer)
Wikipage revision ID	1111959480 (xsd:integer)
Link from a Wikipage to another Wikipage	-algebra Mathematics Gelfand representation Quantum groups Hopf algebra Topological group Tensor product C-algebras Coalgebra Homeomorphism Hopf algebras C*-algebra Group representation Kronecker delta Unitary representation S. L. Woronowicz Noncommutative geometry
sameAs	Compact quantum group Compact quantum group Compact quantum group Compact quantum group
dbp:wikiPageUsesTemplate	dbt:= dbt:Math dbt:More_citations_needed dbt:Mvar dbt:Reflist dbt:Short_description
has abstract	In mathematics, a compact quantum group is an abstract structure on a unital separable C-algebra axiomatized from those that exist on the commutative C-algebra of "continuous complex-valued functions" on a compact quantum group. The basic motivation for this theory comes from the following analogy. The space of complex-valued functions on a compact Hausdorff topological space forms a commutative C-algebra. On the other hand, by the Gelfand Theorem, a commutative C-algebra is isomorphic to the C-algebra of continuous complex-valued functions on a compact Hausdorff topological space, and the topological space is uniquely determined by the C-algebra up to homeomorphism. S. L. Woronowicz introduced the important concept of compact matrix quantum groups, which he initially called compact pseudogroups. Compact matrix quantum groups are abstract structures on which the "continuous functions" on the structure are given by elements of a C*-algebra. The geometry of a compact matrix quantum group is a special case of a noncommutative geometry. (en)
gold:hypernym	Structure
prov:wasDerivedFrom	wikipedia-en:Compact_quantum_group?oldid=1111959480&ns=0
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foaf:isPrimaryTopicOf	wikipedia-en:Compact_quantum_group
is Link from a Wikipage to another Wikipage of	Locally compact quantum group Quantum group
is foaf:primaryTopic of	wikipedia-en:Compact_quantum_group

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