Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups

DOI10.1007/s00006-012-0371-3zbMath1273.15021arXiv1205.1451OpenAlexW2134927509MaRDI QIDQ351484

Pierre-Philippe Dechant

Publication date: 5 July 2013

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.1451

zbMATH Keywords

representationCoxeter grouproot systemquaternionsClifford algebraspinorClifford geometric algebrabinary polyhedral groupClifford geometric product

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Clifford algebras, spinors (15A66)

Related Items (9)

Clifford algebra is the natural framework for root systems and Coxeter groups. Group theory: Coxeter, conformal and modular groups ⋮ The \(E_8\) geometry from a Clifford perspective ⋮ The quaternion domain Fourier transform and its properties ⋮ Platonic solids generate their four-dimensional analogues ⋮ Affine extensions of non-crystallographic Coxeter groups induced by projection ⋮ From the Trinity ( A ₃ , B ₃ , H ₃ ) to an ADE correspondence ⋮ A Clifford algebraic framework for Coxeter group theoretic computations. ⋮ Clifford spinors and root system induction: \(H_4\) and the grand antiprism ⋮ Binary icosahedral group and 600-cell

Uses Software

• CLUCalc

Cites Work

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