Fricke identities, Frobenius $k$-characters and Markov equation

Abstract

In 1896 Frobenius and Fricke had published two seemingly unrelated papers: Frobenius had started to develop his theory of $k$-characters for finite groups motivated by Dedekind's question about factorisation of the group determinant, while Fricke followed Klein's approach to the uniformization theorem. We show that in fact these two works can be naturally linked and both are related to remarkable Markov's paper of 1880 on arithmetic of binary quadratic forms.

11 pages, contribution to Boris Dubrovin memorial volume

References in corpus (3)

• The Modular Group Action on Real SL(2)-characters of a One-Holed Torus
• Rings of continuous functions, symmetric products, and Frobenius algebras
• Markoff Surfaces and Strong Approximation: 1