special linear group

Given a vector spaceMathworldPlanetmath V, the special linear groupMathworldPlanetmath SL(V) is defined to be the subgroupMathworldPlanetmathPlanetmath of the general linear groupMathworldPlanetmath GL(V) consisting of all invertible linear transformations T:VV in GL(V) that have determinantMathworldPlanetmath 1.

If V=𝔽n for some field 𝔽, then the group SL(V) is often denoted SL(n,𝔽) or SLn(𝔽), and if one identifies each linear transformation with its matrix with respect to the standard basis, then SL(n,𝔽) consists of all n×n matrices with entries in 𝔽 that have determinant 1.

Title special linear group
Canonical name SpecialLinearGroup
Date of creation 2013-03-22 12:25:38
Last modified on 2013-03-22 12:25:38
Owner djao (24)
Last modified by djao (24)
Numerical id 7
Author djao (24)
Entry type Definition
Classification msc 20G15
Synonym SL
Related topic GeneralLinearGroup
Related topic Group
Related topic UnimodularMatrix