On bilinear algorithms for multiplication in quaternion algebras

TL;DR

This paper determines that the bilinear complexity of multiplication in non-split quaternion algebras over fields with characteristic not 2 is exactly 8, contributing to the understanding of algebraic multiplication complexity.

Contribution

It establishes the exact bilinear complexity for multiplication in non-split quaternion algebras, advancing the characterization of algebras with near-minimal rank.

Findings

Bilinear complexity in non-split quaternion algebras is 8

Provides a translation of prior research report

Advances understanding of algebraic multiplication complexity

Abstract

We show that the bilinear complexity of multiplication in a non-split quaternion algebra over a field of characteristic distinct from 2 is 8. This question is motivated by the problem of characterising algebras of almost minimal rank studied by Blaeser and de Voltaire in [1]. This paper is a translation of a report submitted by the author to the XI international seminar "Discrete mathematics and applications" (in Russian).