The work of Chevalley in Lie groups and algebraic groups

2001 ◽  
pp. 147-148
Keyword(s):  
Lie Groups ◽  
Algebraic Groups

Algebraic Groups and Lie Groups with Few Factors

2008 ◽  
Author(s):  
Alfonso Di Bartolo ◽  
Giovanni Falcone ◽  
Peter Plaumann ◽  
Karl Strambach
Keyword(s):  
Lie Groups ◽  
Algebraic Groups

scholarly journals Locally compact groups with every isometric action bounded or proper

2018 ◽  
Vol 12 (02) ◽  
pp. 267-292
Author(s):  
Romain Tessera ◽  
Alain Valette
Keyword(s):  
Lie Groups ◽  
Local Field ◽  
Algebraic Groups ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Isometric Action ◽  
Locally Compact ◽  
Linear Algebraic Groups ◽  
Isometric Actions

A locally compact group [Formula: see text] has property PL if every isometric [Formula: see text]-action either has bounded orbits or is (metrically) proper. For [Formula: see text], say that [Formula: see text] has property BPp if the same alternative holds for the smaller class of affine isometric actions on [Formula: see text]-spaces. We explore properties PL and BPp and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including nonlinear ones.

Lie Groups and Algebraic Groups

1990 ◽  
Author(s):  
Arkadij L. Onishchik ◽  
Ernest B. Vinberg
Keyword(s):  
Lie Groups ◽  
Algebraic Groups

Lie Groups and Algebraic Groups

2017 ◽  
pp. 524-539
Author(s):  
James Carlson ◽  
Stefan Muller-Stach ◽  
Chris Peters
Keyword(s):  
Lie Groups ◽  
Algebraic Groups

scholarly journals On orbits of algebraic groups and Lie groups

1982 ◽  
Vol 25 (1) ◽  
pp. 1-28 ◽  
Author(s):  
R.W. Richardson
Keyword(s):  
Fixed Points ◽  
Homogeneous Space ◽  
Algebraic Group ◽  
Lie Groups ◽  
Lie Group ◽  
Closed Subgroup ◽  
Algebraic Groups ◽  
General Situation ◽  
Coset Space ◽  
Identity Component

In this paper we will be concerned with orbits of a closed subgroup Z of an algebraic group (respectively Lie group) G on a homogeneous space X for G. More precisely, let D be a closed subgroup of G and let X denote the coset space G/D. Let S be a subgroup of G and let Z denote (GS)0 the identity component of GS, the centralizer of S in G. We consider the orbits of Z on XS, the set of fixed points of S on X. We also treat the more general situation in which S is an algebraic group (respectively Lie group) which acts on G by automorphisms and acts on X compatibly with the action of G; again we consider the orbits of (GS)0 on XS.

scholarly journals Some complements to the Lazard isomorphism

2010 ◽  
Vol 147 (1) ◽  
pp. 235-262 ◽  
Author(s):  
Annette Huber ◽  
Guido Kings ◽  
Niko Naumann
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Algebraic Groups ◽  
Group Cohomology ◽  
Continuous Group ◽  
Lie Algebra Cohomology ◽  
Seminal Work

AbstractLazard showed in his seminal work (Groupes analytiques p-adiques, Publ. Math. Inst. Hautes Études Sci. 26 (1965), 389–603) that for rational coefficients, continuous group cohomology of p-adic Lie groups is isomorphic to Lie algebra cohomology. We refine this result in two directions: first, we extend Lazard’s isomorphism to integral coefficients under certain conditions; and second, we show that for algebraic groups over finite extensions K/ℚp, his isomorphism can be generalized to K-analytic cochains andK-Lie algebra cohomology.

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