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connected subgroup

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  • Maximal compact subgroup — In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups. Maximal compact subgroups play an important role in the classification of …   Wikipedia

  • Cartan subgroup — In mathematics, a Cartan subgroup of a Lie group or algebraic group G is one of the subgroups whose Lie algebrais a Cartan subalgebra. The dimension of a Cartan subgroup, and therefore of a Cartan subalgebra, is the rank of G .ConventionsThe… …   Wikipedia

  • Borel subgroup — In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup. For example, in the group GLn (n x n invertible matrices), the subgroup of invertible upper… …   Wikipedia

  • Analytic subgroup — The analytic subgroup is an important concept in mathematics (in Lie group theory). [Knapp, Anthony W. : Lie groups Beyond an Introduction, Second Edition.] [citebook|title=Theory of Lie Groups |author= Claude Chevalley|year=… …   Wikipedia

  • Hyperspecial subgroup — In the theory of reductive groups over local fields, a hyperspecial subgroup of a reductive group G is a certain type of compact subgroup of G .In particular, let F be a nonarchimedean local field, O its ring of integers, k its residue field and… …   Wikipedia

  • No small subgroup — In mathematics, especially in topology, a topological group G is said to have no small subgroup if there exists a neighborhood U of the identity that contains no nontrivial subgroup of G. An abbreviation NSS is sometimes used. A basic example of… …   Wikipedia

  • Lie group — Lie groups …   Wikipedia

  • Spin group — In mathematics the spin group Spin( n ) is the double cover of the special orthogonal group SO( n ), such that there exists a short exact sequence of Lie groups:1 o mathbb{Z} 2 o operatorname{Spin}(n) o operatorname{SO}(n) o 1.For n gt; 2, Spin(… …   Wikipedia

  • Hilbert's fifth problem — Hilbert s fifth problem, from the Hilbert problems list promulgated in 1900 by David Hilbert, concerns the characterization of Lie groups. The theory of Lie groups describes continuous symmetry in mathematics; its importance there and in… …   Wikipedia

  • Laplace–Runge–Lenz vector — Throughout this article, vectors and their magnitudes are indicated by boldface and italic type, respectively; for example, left| mathbf{A} ight| = A. In classical mechanics, the Laplace–Runge–Lenz vector (or simply the LRL vector) is a vector… …   Wikipedia

  • Hidehiko Yamabe — (jap. 山辺 英彦, Yamabe Hidehiko; * 22. August 1923 in Ashiya, Präfektur Hyōgo; † 20. November 1960 in Evanston, Illinois) war ein japanischer Mathematiker. Inhaltsverzeichnis 1 Leben 2 Werk …   Deutsch Wikipedia

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