Fricke's trace identity and spin groups

Matthew de Courcy-Ireland

Fricke's trace identity and spin groups

Group Theory 2026-07-20 v1 Number Theory Representation Theory

Authors: Matthew de Courcy-Ireland

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.

Cite

@article{arxiv.2607.18167,
  title  = {Fricke's trace identity and spin groups},
  author = {Matthew de Courcy-Ireland},
  journal= {arXiv preprint arXiv:2607.18167},
  year   = {2026}
}

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13 pages