Essays in the History of Lie Groups and Algebraic Groups

First we introduce the history of group theory. Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. Secondly, we give the main classes of groups: permutation groups, matrix groups, transformation groups, abstract groups and topological and algebraic groups. Finally, we give two different presentations of a group: combinatorial group theory and geometric group theory.

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The Work of Chevalley in Lie Groups and Algebraic Groups

Springer Collected Works in Mathematics - Oeuvres - Collected Papers IV ◽

10.1007/978-3-642-41240-0_19 ◽

2001 ◽

pp. 309-330

Author(s):

Armand Borel

Keyword(s):

Lie Groups ◽

Algebraic Groups

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The work of Chevalley in Lie groups and algebraic groups

History of Mathematics - Essays in the History of Lie Groups and Algebraic Groups ◽

10.1090/hmath/021/07 ◽

2001 ◽

pp. 147-148

Keyword(s):

Lie Groups ◽

Algebraic Groups

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Algebraic Groups and Lie Groups with Few Factors

10.1007/978-3-540-78584-2 ◽

2008 ◽

Cited By ~ 3

Author(s):

Alfonso Di Bartolo ◽

Giovanni Falcone ◽

Peter Plaumann ◽

Karl Strambach

Keyword(s):

Lie Groups ◽

Algebraic Groups

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Locally compact groups with every isometric action bounded or proper

Journal of Topology and Analysis ◽

10.1142/s1793525319500547 ◽

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.

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