The magic square of Lie groups: the $2\times 2$ case

Abstract

A unified treatment of the $2\times 2$ analog of the Freudenthal-Tits magic square of Lie groups is given, providing an explicit representation in terms of matrix groups over composition algebras.

arXiv comment22 pages, 1 figure. Archive of paper published in 2014

References in corpus (9)

• Finite Lorentz Transformations, Automorphisms, and Division Algebras
• Octonions, E6, and Particle Physics
• Dimensional Reduction
• The general classical solution of the superparticle
• The Structure of E6
• E6, the Group: The structure of SL(3,O)
• Division Algebra Representations of SO(4,2)
• Discovering Real Lie Subalgebras of e6 using Cartan Decompositions
• A Symplectic Representation of ${\mathrm{E}}_7$

Cited by in corpus (8)

• Octions: An $E_8$ description of the Standard Model
• Spin(11,3), particles and octonions
• An octonionic construction of $E_8$ and the Lie algebra magic square
• Klein and Conformal Superspaces, Split Algebras and Spinor Orbits
• The symplectic origin of conformal and Minkowski superspaces
• A New Division Algebra Representation of $E_7$
• A New Division Algebra Representation of $E_6$
• A Proposed $E_8\times E_8$ Kinematic Scaffolding for the Standard Model with Pre-Gravitation