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- Q1000120 subject Q8653251.
- Q1000120 subject Q8805755.
- Q1000120 abstract "In the mathematical theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups.A torus in a compact Lie group G is a compact, connected, abelian Lie subgroup of G (and therefore isomorphic to the standard torus Tn). A maximal torus is one which is maximal among such subgroups. That is, T is a maximal torus if for any other torus T′ containing T we have T = T′. Every torus is contained in a maximal torus simply by dimensional considerations. A noncompact Lie group need not have any nontrivial tori (e.g. Rn).The dimension of a maximal torus in G is called the rank of G. The rank is well-defined since all maximal tori turn out to be conjugate. For semisimple groups the rank is equal to the number of nodes in the associated Dynkin diagram.".
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- Q1000120 wikiPageWikiLink Q8653251.
- Q1000120 wikiPageWikiLink Q8805755.
- Q1000120 wikiPageWikiLink Q936434.
- Q1000120 comment "In the mathematical theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups.A torus in a compact Lie group G is a compact, connected, abelian Lie subgroup of G (and therefore isomorphic to the standard torus Tn). A maximal torus is one which is maximal among such subgroups. That is, T is a maximal torus if for any other torus T′ containing T we have T = T′.".
- Q1000120 label "Maximal torus".