Crystallographic space groups in geometric algebra

DOI10.1063/1.2426416zbMath1121.82042OpenAlexW2035811475MaRDI QIDQ3442226

Jeremy W. Holt, David Hestenes

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/4c3fe08797a47071c2d7d688c71136ae39b108c7

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Other geometric groups, including crystallographic groups (20H15)

Related Items (12)

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 ⋮ Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups ⋮ Geometric algebras of light cone projective graph geometries ⋮ Conjecture on characterisation of bijective 3D digitized reflections and rotations ⋮ A Clifford algebra-based mathematical model for the determination of critical temperatures in superconductors ⋮ Representation of crystallographic subperiodic groups in Clifford's geometric algebra. ⋮ 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 ⋮ Crystal planes and reciprocal space in Clifford geometric algebra ⋮ The coincidence site lattices in 2D hexagonal lattices using Clifford algebra

Cites Work

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• The design of linear algebra and geometry
• Discrete groups generated by reflections
• Computer Algebra and Geometric Algebra with Applications

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