On the Automorphism Group of a Possible Short Algorithm for Multiplying 3 3 Matrices

Key Points

• The aim is to explore the automorphism groups of algorithms for multiplying 3x3 matrices to discover short multiplication methods.
• Proved the relationship between automorphism groups and symmetric groups
• Analyzed algorithms with bilinear complexity of 23 or less
• Examined isomorphic properties of automorphism groups
• The automorphism group is shown to be isomorphic to a subgroup of the product S_l × S_3
• Identified implications for new short matrix multiplication algorithms
• Mapped symmetries within the framework of existing algorithms