About: Cartan pair     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.org associated with source document(s)
QRcode icon
http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FCartan_pair

In the mathematical fields of Lie theory and algebraic topology, the notion of Cartan pair is a technical condition on the relationship between a reductive Lie algebra and a subalgebra reductive in . A reductive pair is said to be Cartan if the relative Lie algebra cohomology is isomorphic to the tensor product of the characteristic subalgebra and an exterior subalgebra of , where On the level of Lie groups, if G is a compact, connected Lie group and K a closed connected subgroup, there are natural fiber bundles , .

AttributesValues
rdfs:label
  • Cartan pair (en)
rdfs:comment
  • In the mathematical fields of Lie theory and algebraic topology, the notion of Cartan pair is a technical condition on the relationship between a reductive Lie algebra and a subalgebra reductive in . A reductive pair is said to be Cartan if the relative Lie algebra cohomology is isomorphic to the tensor product of the characteristic subalgebra and an exterior subalgebra of , where On the level of Lie groups, if G is a compact, connected Lie group and K a closed connected subgroup, there are natural fiber bundles , . (en)
dcterms:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
Link from a Wikipage to an external page
sameAs
dbp:wikiPageUsesTemplate
has abstract
  • In the mathematical fields of Lie theory and algebraic topology, the notion of Cartan pair is a technical condition on the relationship between a reductive Lie algebra and a subalgebra reductive in . A reductive pair is said to be Cartan if the relative Lie algebra cohomology is isomorphic to the tensor product of the characteristic subalgebra and an exterior subalgebra of , where * , the Samelson subspace, are those primitive elements in the kernel of the composition , * is the primitive subspace of , * is the transgression, * and the map of symmetric algebras is induced by the restriction map of dual vector spaces . On the level of Lie groups, if G is a compact, connected Lie group and K a closed connected subgroup, there are natural fiber bundles , where is the homotopy quotient, here homotopy equivalent to the regular quotient, and . Then the characteristic algebra is the image of , the transgression from the primitive subspace P of is that arising from the edge maps in the Serre spectral sequence of the universal bundle , and the subspace of is the kernel of . (en)
prov:wasDerivedFrom
page length (characters) of wiki page
foaf:isPrimaryTopicOf
is Link from a Wikipage to another Wikipage of
is foaf:primaryTopic of
Faceted Search & Find service v1.17_git139 as of Feb 29 2024


Alternative Linked Data Documents: ODE     Content Formats:   [cxml] [csv]     RDF   [text] [turtle] [ld+json] [rdf+json] [rdf+xml]     ODATA   [atom+xml] [odata+json]     Microdata   [microdata+json] [html]    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (61 GB total memory, 42 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software