On bilinear algorithms for multiplication in quaternion algebras

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).