Composition algebras in symmetric tensor categories

2026/08/05 by Alberto Elduque, Javier Rández-Ibáñez
Mathematics · #math.RA #math.QA #msc:17A75 #msc:18M05

paper · pdf

25 pages

arxiv created 2026/08/05 · arxiv updated 2026/08/06

Abstract

Composition algebras in symmetric tensor categories are defined. The classical results on standard unital composition algebras, as well as the classification of the unital composition superalgebras, are reviewed in light of this definition, and the unital composition algebras in the category Ver₄⁺ (the counterpart to the category of vector superspaces in characteristic 2) are classified.

Citations

• Group schemes and their Lie algebras over a symmetric tensor category
• From octonions to composition superalgebras via tensor categories
• Composition algebras
• Hilbert Basis Theorem and Finite Generation of Invariants in Symmetric Fusion Categories in Positive Characteristic
• An extended Freudenthal Magic Square in characteristic 3
• The Octonions
• The octonions