The amalgamated free product structure of 𝐺𝐿₂(𝐾[𝑋₁,⋯,𝑋_{𝑛}])

Abstract

For any ring R we let E 2 (R) be the subgroup of GL 2 (R) generated by elementary matrices. We let E' 2 (R) be the subgroup of GL 2 (JR) generated by E 2 (R) and the invertible diagonal matrices. We denote by B 2 (R) the lower triangular subgroup of GL 2 (R).