The sextonions and E712 Academic Article uri icon

abstract

  • We fill in the "hole" in the exceptional series of Lie algebras that was observed by Cvitanovic, Deligne, Cohen and deMan. More precisely, we show that the intermediate Lie algebra between e 7 and e 8 satisfies some of the decomposition and dimension formulas of the exceptional simple Lie algebras. A key role is played by the sextonions, a six-dimensional algebra between the quaternions and octonions. Using the sextonions, we show similar results hold for the rows of an expanded Freudenthal magic chart. We also obtain new interpretations of the adjoint variety of the exceptional group G2. 2005 Elsevier Inc. All rights reserved.

published proceedings

  • Advances in Mathematics

altmetric score

  • 3

author list (cited authors)

  • Landsberg, J. M., & Manivel, L.

citation count

  • 24

complete list of authors

  • Landsberg, JM||Manivel, L

publication date

  • March 2006