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In mathematics, a Clifford–Klein form is a double coset space Γ\G/H, where G is a reductive Lie group, H a closed subgroup of G, and Γ a discrete subgroup of G that acts properly discontinuously on the homogeneous space G/H. A suitable discrete subgroup Γ may or may not exist, for a given G and H. If Γ exists, there is the question of whether Γ\G/H can be taken to be a compact space, called a compact Clifford–Klein form. When H is itself compact, classical results show that a compact Clifford–Klein form exists. Otherwise it may not, and there are a number of negative results.

Attributes	Values
rdf:type	yago:WikicatLieGroups yago:Abstraction100002137 yago:Attribute100024264 yago:Group100031264 yago:WikicatHomogeneousSpaces chemical compound yago:Space100028651
rdfs:label	Clifford–Klein form (en)
rdfs:comment	In mathematics, a Clifford–Klein form is a double coset space Γ\G/H, where G is a reductive Lie group, H a closed subgroup of G, and Γ a discrete subgroup of G that acts properly discontinuously on the homogeneous space G/H. A suitable discrete subgroup Γ may or may not exist, for a given G and H. If Γ exists, there is the question of whether Γ\G/H can be taken to be a compact space, called a compact Clifford–Klein form. When H is itself compact, classical results show that a compact Clifford–Klein form exists. Otherwise it may not, and there are a number of negative results. (en)
dcterms:subject	Homogeneous spaces Lie groups
Wikipage page ID	797238 (xsd:integer)
Wikipage revision ID	1075328791 (xsd:integer)
Link from a Wikipage to another Wikipage	Quaternion Moritz Epple Homogeneous space Double coset Lie group Compact space Mathematics Constant curvature Homogeneous spaces Clifford parallel Mathematische Annalen Wilhelm Killing Lie groups Group (mathematics) Semisimple Lie group Space form Killing-Hopf theorem Properly discontinuously Discrete subgroup Karl Schwarzchild Clifford surface W. K. Clifford
Link from a Wikipage to an external page	http://www.digizeitschriften.de/dms/resolveppn/%3FPID=GDZPPN00225333X%7Cdoi=10.1007/bf01206655%7Cs2cid=119473479 https://archive.org/details/arxiv-math0305023
sameAs	Clifford–Klein form Clifford–Klein form Clifford–Klein form
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_journal
has abstract	In mathematics, a Clifford–Klein form is a double coset space Γ\G/H, where G is a reductive Lie group, H a closed subgroup of G, and Γ a discrete subgroup of G that acts properly discontinuously on the homogeneous space G/H. A suitable discrete subgroup Γ may or may not exist, for a given G and H. If Γ exists, there is the question of whether Γ\G/H can be taken to be a compact space, called a compact Clifford–Klein form. When H is itself compact, classical results show that a compact Clifford–Klein form exists. Otherwise it may not, and there are a number of negative results. (en)
gold:hypernym	H
prov:wasDerivedFrom	wikipedia-en:Clifford–Klein_form?oldid=1075328791&ns=0
page length (characters) of wiki page	2776 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Clifford–Klein_form
is Link from a Wikipage to another Wikipage of	Homogeneous space Double coset Coset Clifford-Klein form William Kingdon Clifford A Clifford-Klein form List of Lie groups topics List of things named after Felix Klein A Clifford–Klein form Klein-Clifford space
is Wikipage redirect of	Clifford-Klein form A Clifford-Klein form A Clifford–Klein form Klein-Clifford space
is known for of	William Kingdon Clifford
is known for of	William Kingdon Clifford
is foaf:primaryTopic of	wikipedia-en:Clifford–Klein_form

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