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Linear and Nonlinear Group Actions, and the Newton Institute Program

  • Chapter
Algebraic Groups and their Representations

Part of the book series: NATO ASI Series ((ASIC,volume 517))

Abstract

One of the simplest and most useful notions in mathematics is that of a group action: if G is a group and X is a nonempty set, then an action of G on X (or a G-set structure on X) consists of a multiplication operation G × X → X, with the image of a pair (g, x) written as, say, gx, with the following axioms satisfied:

  1. (1)

    lx = x for all x ∈ X (here 1 ∈ G is the identity element of G);

  2. (2)

    (gh)x = g(hx) for all g,h ∈ G and all x ∈ X.

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Authors and Affiliations

  1. Department of Mathematics, The University of Virginia, Charlottesville, VA, 22903, USA

    Leonard Scott

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  1. Mathematics Institute, University of Warwick, Coventry, UK

    R. W. Carter

  2. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK

    J. Saxl

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Scott, L. (1998). Linear and Nonlinear Group Actions, and the Newton Institute Program. In: Carter, R.W., Saxl, J. (eds) Algebraic Groups and their Representations. NATO ASI Series, vol 517. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5308-9_1

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