special linear group

plural special linear groups

1. group theoryFor 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.

   Hence, all congruent bases induced from a game context belong to the special linear group SL(m).

   2014, Holger Ingmar Meinhardt, The Pre-Kernel as a Tractable Solution for Cooperative Games: An Exercise in Algorithmic Game Theory, Springer, page 100

   2 more examples

   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.

   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

   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.