From the Trinity ( A 3 , B 3 , H 3 ) to an ADE correspondence

DOI10.1098/rspa.2018.0034zbMath1425.92225arXiv1812.02804OpenAlexW3123721820MaRDI QIDQ5243634

Pierre-Philippe Dechant

Publication date: 19 November 2019

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.02804

zbMATH Keywords

Coxeter grouproot systemClifford algebratrinityCoxeter planeADE correspondence

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Clifford algebras, spinors (15A66) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10)

Related Items (2)

Generalized cohomological field theories in the higher order formalism ⋮ Clifford spinors and root system induction: \(H_4\) and the grand antiprism

Uses Software

• CLUCalc

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups
• Interactive 3D space group visualization with CLUCalc and the Clifford geometric algebra description of space groups.
• A Clifford algebraic framework for Coxeter group theoretic computations.
• Clifford algebra to geometric calculus. A unified language for mathematics and physics
• New foundations for classical mechanics.
• 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
• Wave equations in conformal space
• Square Roots of –1 in Real Clifford Algebras
• Novel Kac–Moody-type affine extensions of non-crystallographic Coxeter groups
• A 3D Spinorial View of 4D Exceptional Phenomena
• Crystallographic space groups in geometric algebra
• Simple transitive 2-representations of small quotients of Soergel bimodules
• Notes on the K3 Surface and the Mathieu GroupM₂₄
• Affine extensions of non-crystallographic Coxeter groups induced by projection
• Moonshine beyond the Monster

This page was built for publication: From the Trinity ( A ₃ , B ₃ , H ₃ ) to an ADE correspondence