English

The discriminant Pfister form of an algebra with involution of capacity four

Rings and Algebras 2024-09-17 v3 K-Theory and Homology

Abstract

To an orthogonal or unitary involution on a central simple algebra of degree 4, or to a symplectic involution on a central simple algebra of degree 8, we associate a Pfister form that characterises the decomposability of the algebra with involution. In this way we obtain a unified approach to known decomposability criteria for several cases, and a new result for symplectic involutions on degree 88 algebras in characteristic 2.

Keywords

Cite

@article{arxiv.2008.08953,
  title  = {The discriminant Pfister form of an algebra with involution of capacity four},
  author = {Karim Johannes Becher and Nicolas Grenier-Boley and Jean-Pierre Tignol},
  journal= {arXiv preprint arXiv:2008.08953},
  year   = {2024}
}