Magic squares and matrix models of Lie algebras
By C. H. Barton, A. Sudbery. 2002
123 citations recorded by the source corpus.
This paper is concerned with the description of exceptional simple Lie algebras as octonionic analogues of the classical matrix Lie algebras. We review the Tits–Freudenthal construction of the magic square, which includes the exceptional Lie algebras as the octonionic case of a construction in terms of a Jordan algebra of hermitian 3×3 matrices (Tits) or various plane and other geometries (Freudenthal). We present alternative constructions of the magic square which explain its symmetry, and show explicitly how the use of split composition algebras leads to analogues of the matrix Lie algebras su(3),sl(3) and sp(6). We adapt the magic square construction to include analogues of su(2),sl(2) and sp(4) for all real division algebras.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/f3dd64f25251fd825f64a80071400fd20bccf12b
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In Algebra and Number Theory
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Citations in the corpus
- The Magic Square and Symmetric Compositions (2004, background): “> > Barton and Sudbery [4, (4.1)] consider the Lie algebra Tri C = {(f, g, h) ∈ o(C, q)3 : f(xy) = xg(y) + h(x)y ∀x, y ∈ C} , while Allison and Faulkner [2, Section 3] consider t(C) = {(f, g, h) ∈ o(C, q)3 : f̄(xy) = g(x)y + xh(y) ∀x, y ∈ C} .”