English

Colour algebras over rings

Rings and Algebras 2026-03-09 v2

Abstract

Colour algebras over fields of odd characteristic are well-known noncommutative Jordan algebras. We define colour algebras more generally over a unital commutative associative ring with 12R\frac{1}{2}\in R, and show that colour algebras can be constructed canonically by employing nondegenerate ternary hermitian forms with trivial determinant. We investigate their structure, automorphism group and derivations. As over fields, colour algebras over RR are closely related to octonion algebras over RR.

Keywords

Cite

@article{arxiv.2409.14574,
  title  = {Colour algebras over rings},
  author = {Susanne Pumpluen},
  journal= {arXiv preprint arXiv:2409.14574},
  year   = {2026}
}

Comments

10 pages

R2 v1 2026-06-28T18:53:04.545Z