Composition algebras in symmetric tensor categories

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 $Ve{r}_4^{+}$ (the counterpart to the category of vector superspaces in characteristic 2) are classified.

25 pages