Composition algebras in symmetric tensor categories

Alberto Elduque; Javier Rández-Ibáñez

Composition algebras in symmetric tensor categories

Rings and Algebras 2026-08-05 v1 Quantum Algebra

Authors: Alberto Elduque , Javier Rández-Ibáñez

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 $Ver_4^+$ (the counterpart to the category of vector superspaces in characteristic 2) are classified.

Cite

@article{arxiv.2608.04668,
  title  = {Composition algebras in symmetric tensor categories},
  author = {Alberto Elduque and Javier Rández-Ibáñez},
  journal= {arXiv preprint arXiv:2608.04668},
  year   = {2026}
}

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25 pages