On the lengths of Okubo algebras

Alexander Guterman; Svetlana Zhilina

On the lengths of Okubo algebras

Rings and Algebras 2023-12-07 v1

Authors: Alexander Guterman , Svetlana Zhilina

Abstract

We compute the lengths of two particular cases of (possibly non-unital) composition algebras, namely, standard composition algebras and Okubo algebras over an arbitrary field $\mathbb{F}$ . These results finish the complete description of lengths of symmetric composition algebras and finite-dimensional flexible composition algebras.

Keywords

Okubo algebras composition algebras lengths symmetric composition algebras flexible composition algebras non-unital algebras

Cite

@article{arxiv.2312.03174,
  title  = {On the lengths of Okubo algebras},
  author = {Alexander Guterman and Svetlana Zhilina},
  journal= {arXiv preprint arXiv:2312.03174},
  year   = {2023}
}

Comments

22 pages

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