A Clifford Algebraic Framework for Coxeter Group Theoretic Computations

@article{Dechant2014ACA,
  title={A Clifford Algebraic Framework for Coxeter Group Theoretic Computations},
  author={Pierre-Philippe Dechant},
  journal={Advances in Applied Clifford Algebras},
  year={2014},
  volume={24},
  pages={89-108}
}
  • Pierre-Philippe Dechant
  • Published 2014
  • Mathematics, Physics
  • Advances in Applied Clifford Algebras
  • Real physical systems with reflective and rotational symmetries such as viruses, fullerenes and quasicrystals have recently been modeled successfully in terms of three-dimensional (affine) Coxeter groups. Motivated by this progress, we explore here the benefits of performing the relevant computations in a Geometric Algebra framework, which is particularly suited to describing reflections. Starting from the Coxeter generators of the reflections, we describe how the relevant chiral (rotational… CONTINUE READING
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    References

    SHOWING 1-10 OF 72 REFERENCES
    Clifford Algebra Unveils a Surprising Geometric Significance of Quaternionic Root Systems of Coxeter Groups
    • 16
    • PDF
    Affine extensions of non-crystallographic Coxeter groups induced by projection
    • 23
    • PDF
    Polyhedra obtained from Coxeter groups and quaternions
    • 22
    Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups
    • 20
    • PDF
    Platonic solids generate their four-dimensional analogues.
    • 10
    • PDF
    Rank-3 root systems induce root systems of rank 4 via a new Clifford spinor construction
    • 9
    • PDF
    A covariant approach to geometry using geometric algebra
    • 29
    • PDF
    Quaternionic Roots of E 8 Related Coxeter Graphs and Quasicrystals
    • 10
    • PDF
    Interactive 3D Space Group Visualization with CLUCalc and the Clifford Geometric Algebra Description of Space Groups
    • 22
    • PDF
    Catalan solids derived from three-dimensional-root systems and quaternions
    • 24
    • PDF