An exposition of results of Fricke

2004/02/06 by William M. Goldman, Goldman, William M.
Engineering · Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Physics and Engineering Research Articles #Rings and Algebras (math.RA) #math.GM #math.RA

paper · pdf · doi:10.48550/arxiv.math/0402103

openalex publication_date 2004/02/06 · arxiv created 2005/09/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives an elementary proof of the result that the conjugacy classes of pairs (X,Y) of unimodular 2x2 complex matrices is an affine 3-space, parametrized by the traces of X, Y and XY. Identities for triples of elements of SL(2,C) are also derived.

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