special linear group

English

Noun

special linear group (plural special linear groups)

  1. (group theory) For given field F and order n, the group of n×n matrices with determinant 1, with the group operations of matrix multiplication and matrix inversion.
    • 1972, Johan G. F. Belinfante, Bernard Kolman, A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods, Society for Industrial and Applied Mathematics, page 6,
      The complex special linear group SL(n, C) is the subgroup of GL(n, C) consisting of matrices with determinant one. […] The special linear groups are sometimes also called unimodular groups.
    • 1998, F. Celler, C. R. Leedham-Green, A constructive recognition algorithm for the special linear group, Robert Curtis, Robert Wilson (editors), The Atlas of Finite Groups: Ten Years On, Cambridge University Press, 2003 Digitally Printed Edition, page 11,
      In the first part of this note we present an algorithm to recognise constructively the special linear group.
    • 2014, Holger Ingmar Meinhardt, The Pre-Kernel as a Tractable Solution for Cooperative Games: An Exercise in Algorithmic Game Theory, Springer, page 100,
      Hence, all congruent bases induced from a game context belong to the special linear group SL(m).

Usage notes

The special linear group can be denoted SL(n, F) or SLn(F) — or, if the field is understood, SL(n) or SLn. It is a normal subgroup of the general linear group GL(n,F). In the cases that F is the field of real or of complex numbers, SL(n, F) is a Lie group.

Derived terms
  • projective special linear group

Translations

See also

Further reading
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