On automorphism group of a possible short algorithm for multiplication of $3\times3$ matrices
Abstract
Studying algorithms admitting nontrivial symmetries is a prospective way of constructing new short algorithms of matrix multiplication. The main result of the article is that if there exists an algorithm of multiplicative length $l\leq22$ for multuplication of $3\times3$ matrices then its automorphism group is isomorphic to a subgroup of $S_l\times S_3$.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2211.06485
 arXiv:
 arXiv:2211.06485
 Bibcode:
 2022arXiv221106485B
 Keywords:

 Computer Science  Computational Complexity;
 Mathematics  Group Theory;
 68Q25 (Primary);
 20C99 (Secondary);
 F.2
 EPrint:
 11 pp. To be submitted to European J. Math