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In mathematics, KK-theory is a common generalization both of K-homology and K-theory as an additive bivariant functor on separable C*-algebras. This notion was introduced by the Russian mathematician in 1980. KK-theory was followed by a series of similar bifunctor constructions such as the E-theory and the , most of them having more category-theoretic flavors, or concerning another class of algebras rather than that of the separable C*-algebras, or incorporating group actions.

Attributes	Values
rdfs:label	KK-Theorie (de) KK-theory (en)
rdfs:comment	Die KK-Theorie ist eine mathematische Theorie aus dem Bereich der Funktionalanalysis. Der Name rührt daher, dass sie eine K-Theorie mit zwei Variablen darstellt, die die klassische K-Theorie für C-Algebren und die Theorie der Erweiterungen von C-Algebren verallgemeinert. Die KK-Theorie geht auf G. G. Kasparow zurück. (de) In mathematics, KK-theory is a common generalization both of K-homology and K-theory as an additive bivariant functor on separable C-algebras. This notion was introduced by the Russian mathematician in 1980. KK-theory was followed by a series of similar bifunctor constructions such as the E-theory and the , most of them having more category-theoretic flavors, or concerning another class of algebras rather than that of the separable C-algebras, or incorporating group actions. (en)
dcterms:subject	K-theory C*-algebras
Wikipage page ID	13314087 (xsd:integer)
Wikipage revision ID	888200140 (xsd:integer)
Link from a Wikipage to another Wikipage	Ronald G. Douglas Cup product C-algebras Mathematics Nuclear C-algebra Separable space Operator K-theory Baum–Connes conjecture Functor Ideal (ring theory) Noncommutative topology K-theory K-homology Lawrence G. Brown Group action (mathematics) Atiyah–Singer index theorem Isomorphic C-algebras Joachim Cuntz C-algebra Fredholm module Cap product Category (mathematics) Category theory Bott periodicity Hilbert module dbr:Gennadi_Kasparov dbr:Bivariant_periodic_cyclic_theory dbr:Split-exact
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=wfoCkgAACAAJ
sameAs	KK-theory KK-theory KK-theory KK-theory KK-theory
dbp:wikiPageUsesTemplate	dbt:About dbt:Nlab dbt:Refbegin dbt:Refend dbt:Reflist
has abstract	Die KK-Theorie ist eine mathematische Theorie aus dem Bereich der Funktionalanalysis. Der Name rührt daher, dass sie eine K-Theorie mit zwei Variablen darstellt, die die klassische K-Theorie für C-Algebren und die Theorie der Erweiterungen von C-Algebren verallgemeinert. Die KK-Theorie geht auf G. G. Kasparow zurück. (de) In mathematics, KK-theory is a common generalization both of K-homology and K-theory as an additive bivariant functor on separable C-algebras. This notion was introduced by the Russian mathematician in 1980. It was influenced by Atiyah's concept of Fredholm modules for the Atiyah–Singer index theorem, and the classification of extensions of C-algebras by Lawrence G. Brown, Ronald G. Douglas, and Peter Arthur Fillmore in 1977. In turn, it has had great success in operator algebraic formalism toward the index theory and the classification of nuclear C-algebras, as it was the key to the solutions of many problems in operator K-theory, such as, for instance, the mere calculation of K-groups. Furthermore, it was essential in the development of the Baum–Connes conjecture and plays a crucial role in noncommutative topology. KK-theory was followed by a series of similar bifunctor constructions such as the E-theory and the , most of them having more category-theoretic flavors, or concerning another class of algebras rather than that of the separable C-algebras, or incorporating group actions. (en)
gold:hypernym	Generalization
prov:wasDerivedFrom	wikipedia-en:KK-theory?oldid=888200140&ns=0
page length (characters) of wiki page	7113 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:KK-theory
is Link from a Wikipage to another Wikipage of	Projectionless C-algebra Cyclic homology KK-Theory Glossary of areas of mathematics Mythology Operator K-theory Baum–Connes conjecture Noncommutative topology K-theory Hilbert C-module Topological K-theory KK E-theory
is Wikipage redirect of	KK-Theory E-theory
is Wikipage disambiguates of	KK
is foaf:primaryTopic of	wikipedia-en:KK-theory

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