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Statements

Subject Item
dbr:Universal_C*-algebra
rdfs:label
Universal C*-algebra
rdfs:comment
In mathematics, a universal C*-algebra is a C*-algebra described in terms of generators and relations. In contrast to rings or algebras, where one can consider quotients by free rings to construct universal objects, C*-algebras must be realizable as algebras of bounded operators on a Hilbert space by the Gelfand-Naimark-Segal construction and the relations must prescribe a uniform bound on the norm of each generator. This means that depending on the generators and relations, a universal C*-algebra may not exist. In particular, free C*-algebras do not exist.
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dbc:C*-algebras
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668934
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1008251431
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dbr:Free_algebra dbr:Full_subcategory dbr:Fields_Institute_Monographs dbr:Continuous_functional_calculus dbr:Algebra_over_a_field dbr:Seminorm dbc:C*-algebras dbr:Gelfand-Naimark-Segal_construction dbr:Category_(mathematics) dbr:Ring_(mathematics) dbr:K-graph_C*-algebras dbr:Quotient_ring dbr:C*-algebra dbr:Partial_isometry dbr:Noncommutative_torus dbr:American_Mathematical_Society dbr:Cuntz_algebra dbr:Graph_C*-algebras dbr:Free_ring dbr:Mathematics
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In mathematics, a universal C*-algebra is a C*-algebra described in terms of generators and relations. In contrast to rings or algebras, where one can consider quotients by free rings to construct universal objects, C*-algebras must be realizable as algebras of bounded operators on a Hilbert space by the Gelfand-Naimark-Segal construction and the relations must prescribe a uniform bound on the norm of each generator. This means that depending on the generators and relations, a universal C*-algebra may not exist. In particular, free C*-algebras do not exist.
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dbr:Algebra
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wikipedia-en:Universal_C*-algebra?oldid=1008251431&ns=0
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wikipedia-en:Universal_C*-algebra