About: Spectral triple

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric phenomenon in an analytic way. The definition typically involves a Hilbert space, an algebra of operators on it and an unbounded self-adjoint operator, endowed with supplemental structures. It was conceived by Alain Connes who was motivated by the Atiyah-Singer index theorem and sought its extension to 'noncommutative' spaces. Some authors refer to this notion as unbounded K-cycles or as unbounded Fredholm modules.

Property Value
dbo:abstract
  • In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric phenomenon in an analytic way. The definition typically involves a Hilbert space, an algebra of operators on it and an unbounded self-adjoint operator, endowed with supplemental structures. It was conceived by Alain Connes who was motivated by the Atiyah-Singer index theorem and sought its extension to 'noncommutative' spaces. Some authors refer to this notion as unbounded K-cycles or as unbounded Fredholm modules. (en)
  • 비가환 기하학에서 스펙트럼 삼조(spectrum三組, 영어: spectral triple)는 스핀 다양체의 개념의 비가환 일반화이다. (ko)
dbo:wikiPageExternalLink
dbo:wikiPageID
  • 23856672 (xsd:integer)
dbo:wikiPageLength
  • 8231 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1027755512 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
gold:hypernym
rdfs:comment
  • In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric phenomenon in an analytic way. The definition typically involves a Hilbert space, an algebra of operators on it and an unbounded self-adjoint operator, endowed with supplemental structures. It was conceived by Alain Connes who was motivated by the Atiyah-Singer index theorem and sought its extension to 'noncommutative' spaces. Some authors refer to this notion as unbounded K-cycles or as unbounded Fredholm modules. (en)
  • 비가환 기하학에서 스펙트럼 삼조(spectrum三組, 영어: spectral triple)는 스핀 다양체의 개념의 비가환 일반화이다. (ko)
rdfs:label
  • 스펙트럼 삼조 (ko)
  • Spectral triple (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageRedirects of
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License