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Sextonions and the Magic Square
Author(s) -
Westbury Bruce W.
Publication year - 2006
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610706022605
Subject(s) - magic square , subalgebra , magic (telescope) , mathematics , quaternion , square (algebra) , lie algebra , algebra over a field , pure mathematics , combinatorics , physics , geometry , quantum mechanics
Associated to any complex simple Lie algebra is a non‐reductive complex Lie algebra which we call the intermediate Lie algebra. We propose that these algebras can be included in both the magic square and the magic triangle to give an additional row and column. The extra row and column in the magic square correspond to the sextonions. This is a six‐dimensional subalgebra of the split octonions which contains the split quaternions.