Fricke's trace identity and spin groups

2026/07/20 by Matthew de Courcy-Ireland
Mathematics · #math.GR #math.NT #math.RT

paper · pdf

Abstract

We give a proof of Fricke's trace identity using the exceptional spin double cover of an orthogonal group in four variables. We also explain how Fricke's identity is related to the double-angle formula from trigonometry as well as an identity for symplectic matrices.

Related

• On the distribution of the trace in the unitary symplectic group and the distribution of Frobenius
• Fricke identities, Frobenius k-characters and Markov equation
• A simple trace formula for arithmetic groups
• The Gutzwiller Trace Formula for Quantum Systems with Spin
• Ueber Eigenwerte, Integrale und pi²/6: Die Idee der Spurformel (On eigenvalues, integrals and pi²/6: The idea of the trace formula)