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Israel Journal of Mathematics

, Volume 178, Issue 1, pp 187–208 | Cite as

Cayley form, comass, and triality isomorphisms

  • Mikhail G. KatzEmail author
  • Steve Shnider
Article

Abstract

Following an idea of Dadok, Harvey and Morgan, we apply the triality property of Spin(8) to calculate the comass of self-dual 4-forms on ℝ8. In particular, we prove that the Cayley form has comass 1 and that any self-dual 4-form realizing the maximal Wirtinger ratio (equation (1.5)) is SO(8)-conjugate to the Cayley form. We also use triality to prove that the stabilizer in SO(8) of the Cayley form is Spin(7). The results have applications in systolic geometry, calibrated geometry, and Spin(7) manifolds.

Keywords

Weight Space Maximal Torus Dynkin Diagram Cartan Subalgebra Coadjoint Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  1. 1.Department of MathematicsBar Ilan UniversityRamat GanIsrael

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