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Statements

Subject Item
dbr:Regular_element_of_a_Lie_algebra
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yago:WikicatLieAlgebras yago:PsychologicalFeature100023100 yago:Science105999797 yago:Content105809192 yago:WikicatLieGroups yago:Algebra106012726 yago:Discipline105996646 yago:Group100031264 dbo:MilitaryUnit yago:Mathematics106000644 yago:Abstraction100002137 yago:Cognition100023271 yago:KnowledgeDomain105999266 yago:PureMathematics106003682
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Regular element of a Lie algebra
rdfs:comment
In mathematics, a regular element of a Lie algebra or Lie group is an element whose centralizer has dimension as small as possible.For example, in a complex semisimple Lie algebra, an element is regular if its centralizer in has dimension equal to the rank of , which in turn equals the dimension of some Cartan subalgebra (note that in earlier papers, an element of a complex semisimple Lie algebra was termed regular if it is semisimple and the kernel of its adjoint representation is a Cartan subalgebra).An element a Lie group is regular if its centralizer has dimension equal to the rank of .
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dbc:Lie_groups dbc:Lie_algebras
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dbr:Compact_Lie_group dbr:Lie_group dbc:Lie_algebras dbr:Conjugacy_class dbr:Characteristic_polynomial dbr:Engel's_theorem dbc:Lie_groups dbr:Semisimple_Lie_algebra dbr:Adjoint_representation dbr:Springer-Verlag dbr:Adjoint_endomorphism dbr:Complex_number dbr:Zariski_topology dbr:Generalized_eigenspace dbr:Cartan_subalgebra dbr:Algebraic_torus dbr:Lie_algebra dbr:Maximal_torus dbr:Jordan_normal_form
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dbo:abstract
In mathematics, a regular element of a Lie algebra or Lie group is an element whose centralizer has dimension as small as possible.For example, in a complex semisimple Lie algebra, an element is regular if its centralizer in has dimension equal to the rank of , which in turn equals the dimension of some Cartan subalgebra (note that in earlier papers, an element of a complex semisimple Lie algebra was termed regular if it is semisimple and the kernel of its adjoint representation is a Cartan subalgebra).An element a Lie group is regular if its centralizer has dimension equal to the rank of .
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wikipedia-en:Regular_element_of_a_Lie_algebra