Clifford-Klein form

Clifford-Klein form

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.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Clifford–Klein form — In mathematics, a Clifford–Klein form is a double coset space ΓG/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… …   Wikipedia

  • Klein — may refer to:People with the surname Klein: *Klein (surname)In places: *Klein, Montana, community in the United States *Klein, Texas, community in the United States *Klein Betschkerek, community in Romania *Klein Bonaire, island near Bonaire in… …   Wikipedia

  • William Kingdon Clifford — Infobox Scientist name = William Clifford box width = 300px image width = 300px caption = William Kingdon Clifford (1845 1879) birth date = birth date|1845|05|04 birth place = Exeter, Devon, England death date = death date and… …   Wikipedia

  • William Kingdon Clifford — (* 4. Mai 1845 in Exeter, Devon, England; † 3. März 1879 auf Madeira, Portugal) war ein britischer Philosoph und Mathematiker …   Deutsch Wikipedia

  • William Kingdon Clifford — William Kingdon Clifford. William Kingdon Clifford,(4 de Mayo de 1845 3 de Marzo de 1879) fue un matemático inglés que también escribió sobre Filosofía. Junto con Hermann Grassmann es el fundador de lo que ahora se conoce como álgebra geométrica …   Wikipedia Español

  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • List of Lie groups topics — This is a list of Lie group topics, by Wikipedia page. Contents 1 Examples 2 Lie algebras 3 Foundational results 4 Semisimple theory …   Wikipedia

  • List of Lie group topics — This is a list of Lie group topics, by Wikipedia page. Examples See Table of Lie groups for a list *General linear group, special linear group **SL2(R) **SL2(C) *Unitary group, special unitary group **SU(2) **SU(3) *Orthogonal group, special… …   Wikipedia

  • Double coset — In mathematics, an (H,K) double coset in G, where G is a group and H and K are subgroups of G, is an equivalence class for the equivalence relation defined on G by x y if there are h in H and k in K with hxk = y. Then each double coset is of form …   Wikipedia

  • Free regular set — In mathematics, a free regular set is a subset of a topological space that is acted upon disjointly under a given group action. To be more precise, let X be a topological space. Let G be a group of homeomorphisms from X to X. Then we say that the …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”