Non-existence of a short algorithm for multiplication of $3\times3$ matrices with group $S_4\times S_3$, II

Vladimir P. Burichenko

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arXiv · 2211.04032

Non-existence of a short algorithm for multiplication of $3\times3$ matrices with group $S_4\times S_3$, II

Vladimir P. Burichenko

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Abstract

It is proved that there is no an algorithm for multiplication of $3\times3$ matrices of multiplicative length $\leq23$ that is invariant under a certain group isomorphic to $S_4\times S_3$. The proof makes use of description of the orbits of this group on decomposable tensors in the tensor cube $(M_3({\mathbb C}))^{\otimes3}$ which was obtained earlier.

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BibTeX RIS

Vladimir P. Burichenko. 2022-11-08. Non-existence of a short algorithm for multiplication of $3\times3$ matrices with group $S_4\times S_3$, II. https://arxiv.org/abs/2211.04032

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