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- Approximately_finite-dimensional_C*-algebra abstract "In mathematics, an approximately finite-dimensional (AF) C*-algebra is a C*-algebra that is the inductive limit of a sequence of finite-dimensional C*-algebras. Approximate finite-dimensionality was first defined and described combinatorially by Ola Bratteli. Later, George A. Elliott gave a complete classification of AF algebras using the K0 functor whose range consists of ordered abelian groups with sufficiently nice order structure.The classification theorem for AF-algebras serves as a prototype for classification results for larger classes of separable simple nuclear stably finite C*-algebras. Its proof divides into two parts. The invariant here is K0 with its natural order structure; this is a functor. First, one proves existence: a homomorphism between invariants must lift to a *-homomorphism of algebras. Second, one shows uniqueness: the lift must be unique up to approximate unitary equivalence. Classification then follows from what is known as the intertwining argument. For unital AF algebras, both existence and uniqueness follow from the fact the Murray-von Neumann semigroup of projections in an AF algebra is cancellative.The counterpart of simple AF C*-algebras in the von Neumann algebra world are the hyperfinite factors, which were classified by Connes and Haagerup.In the context of noncommutative geometry and topology, AF C*-algebras are noncommutative generalizations of C0(X), where X is a totally disconnected metrizable space.".
- Approximately_finite-dimensional_C*-algebra wikiPageID "17936142".
- Approximately_finite-dimensional_C*-algebra wikiPageLength "22739".
- Approximately_finite-dimensional_C*-algebra wikiPageOutDegree "58".
- Approximately_finite-dimensional_C*-algebra wikiPageRevisionID "702702033".
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Alain_Connes.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Approximate_identity.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Bratteli_diagram.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink C*-algebra.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink CCR_and_CAR_algebras.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Cancellation_property.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Cantor_set.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Category:C*-algebras.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Category_(mathematics).
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Dimension_(vector_space).
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Direct_limit.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Direct_sum_of_modules.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Directed_graph.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Directed_set.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Dyadic_rational.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Elliotts_classification_program.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Functor.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Gelfand_representation.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink George_A._Elliott.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Grothendieck_group.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Mathematics.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Metrization_theorem.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Noncommutative_geometry.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Noncommutative_topology.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Nuclear_C*-algebra.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Ola_Bratteli.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Operator_K-theory.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Partial_isometry.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Partially_ordered_group.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Pascals_triangle.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Projection_(linear_algebra).
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink R.T._Powers.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Semigroup.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Separable_space.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Sequence.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Simple_algebra.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Simple_group.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Spectrum_of_a_C*-algebra.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Topological_K-theory.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Totally_disconnected_space.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Uffe_Haagerup.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Uniformly_hyperfinite_algebra.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink Von_Neumann_algebra.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink File:Elliotts_theorem.png.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink File:Elliotts_theorem_2.png.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLink File:Shen.png.
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLinkText "AF-algebra".
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLinkText "AF-algebras".
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLinkText "Approximately finite-dimensional C*-algebra".
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLinkText "approximately finite-dimensional C*-algebra".
- Approximately_finite-dimensional_C*-algebra wikiPageWikiLinkText "approximately finite-dimensional".
- Approximately_finite-dimensional_C*-algebra date "September 2015".
- Approximately_finite-dimensional_C*-algebra id "p/a110420".
- Approximately_finite-dimensional_C*-algebra reason "Do we require p orthogonal to q, and how does this affect the well-definedness?".
- Approximately_finite-dimensional_C*-algebra title "AF-algebra".
- Approximately_finite-dimensional_C*-algebra wikiPageUsesTemplate Template:Clarify.
- Approximately_finite-dimensional_C*-algebra wikiPageUsesTemplate Template:Clear.
- Approximately_finite-dimensional_C*-algebra wikiPageUsesTemplate Template:Cn.
- Approximately_finite-dimensional_C*-algebra wikiPageUsesTemplate Template:Mapsto.
- Approximately_finite-dimensional_C*-algebra wikiPageUsesTemplate Template:Reflist.
- Approximately_finite-dimensional_C*-algebra wikiPageUsesTemplate Template:Springer.
- Approximately_finite-dimensional_C*-algebra subject Category:C*-algebras.
- Approximately_finite-dimensional_C*-algebra hypernym Algebra.
- Approximately_finite-dimensional_C*-algebra type Algebra.
- Approximately_finite-dimensional_C*-algebra comment "In mathematics, an approximately finite-dimensional (AF) C*-algebra is a C*-algebra that is the inductive limit of a sequence of finite-dimensional C*-algebras. Approximate finite-dimensionality was first defined and described combinatorially by Ola Bratteli. Later, George A.".
- Approximately_finite-dimensional_C*-algebra label "Approximately finite-dimensional C*-algebra".
- Approximately_finite-dimensional_C*-algebra sameAs Q291562.
- Approximately_finite-dimensional_C*-algebra sameAs AF-C*-Algebra.
- Approximately_finite-dimensional_C*-algebra sameAs Algebra_AF.
- Approximately_finite-dimensional_C*-algebra sameAs m.047ql8b.
- Approximately_finite-dimensional_C*-algebra sameAs Q291562.
- Approximately_finite-dimensional_C*-algebra wasDerivedFrom Approximately_finite-dimensional_C*-algebra?oldid=702702033.
- Approximately_finite-dimensional_C*-algebra isPrimaryTopicOf Approximately_finite-dimensional_C*-algebra.
