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In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map p : G → H is a continuous group homomorphism. The map p is called the covering homomorphism. A frequently occurring case is a double covering group, a topological double cover in which H has index 2 in G; examples include the spin groups, pin groups, and metaplectic groups.

Attributes	Values
rdf:type	Thing yago:WikicatLieGroups yago:WikicatTopologicalGroups yago:Abstraction100002137 yago:Group100031264 device
rdfs:label	Grupo de recubrimiento (es) Covering group (en)
rdfs:comment	In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map p : G → H is a continuous group homomorphism. The map p is called the covering homomorphism. A frequently occurring case is a double covering group, a topological double cover in which H has index 2 in G; examples include the spin groups, pin groups, and metaplectic groups. (en) En matemáticas, un grupo de recubrimiento de un grupo topológico H es un espacio recubridor G de H tal que G es un grupo topológico y la aplicación de recubrimiento p:G→H es un homomorfismo de grupos continuo. La aplicación p se dice que abarca el homomorfismo. Un caso frecuente es un grupo de recubrimiento doble, un doble recubrimiento topológico en el que H tiene índice 2 en G; entre sus ejemplos se incluyen los grupos espinoriales, los y el . (es)
rdfs:seeAlso	Group extension
dcterms:subject	Topological groups Lie groups
Wikipage page ID	1378699 (xsd:integer)
Wikipage revision ID	1111511109 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective representation Projective special linear group Metaplectic group Braid group Versor Index of a subgroup Iwasawa decomposition Lie group Compact-open topology Coset Mathematics SO(3) SU(2) Normal subgroup Quotient group SL2(R) Geometrization conjecture Connected space Roots of unity Loop (topology) Short exact sequence Closed set Fundamental group Path (topology) Pin group Spin group Symplectic group Topological groups Center (group theory) Topological group Hausdorff space Lie groups Cyclic group Exponential function Discrete group Double cover (topology) Group action (mathematics) Group homomorphism Covering space Matrix group Abelian group Kernel (group theory) Manifold Special orthogonal group Spin representation Circle group Continuous (topology) Group representation Real number Semilocally simply connected Special linear group Unitary group Principal bundle Tangloids Lie algebras Universal perfect central extension Simply connected Path-connected Smooth map Null-homotopic Locally path-connected dbr:Locally_isomorphic_groups dbr:Path_group
sameAs	Covering group Covering group Covering group Covering group Covering group
dbp:wikiPageUsesTemplate	dbt:About dbt:Cite_book dbt:Cite_journal dbt:See_also dbt:Short_description dbt:Use_American_English
has abstract	In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map p : G → H is a continuous group homomorphism. The map p is called the covering homomorphism. A frequently occurring case is a double covering group, a topological double cover in which H has index 2 in G; examples include the spin groups, pin groups, and metaplectic groups. Roughly explained, saying that for example the metaplectic group Mp2n is a double cover of the symplectic group Sp2n means that there are always two elements in the metaplectic group representing one element in the symplectic group. (en) En matemáticas, un grupo de recubrimiento de un grupo topológico H es un espacio recubridor G de H tal que G es un grupo topológico y la aplicación de recubrimiento p:G→H es un homomorfismo de grupos continuo. La aplicación p se dice que abarca el homomorfismo. Un caso frecuente es un grupo de recubrimiento doble, un doble recubrimiento topológico en el que H tiene índice 2 en G; entre sus ejemplos se incluyen los grupos espinoriales, los y el . Para explicar el concepto en términos generales, se dice que, por ejemplo, el grupo metapléctico Mp2n es un doble recubrimiento del grupo simpléctico Sp2n, lo que significa que siempre hay dos elementos en el grupo metapléctico que representan un elemento en el grupo simpléctico. (es)
gold:hypernym	G
prov:wasDerivedFrom	wikipedia-en:Covering_group?oldid=1111511109&ns=0
page length (characters) of wiki page	11919 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Covering_group
is Link from a Wikipage to another Wikipage of	Projective representation Binasuan Representation theory of the Lorentz group Prehomogeneous vector space 't Hooft loop

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