Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 101-111
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V. P. Burichenko. Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3$, II. Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 101-111. http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a11/
@article{TIMB_2023_31_1_a11,
author = {V. P. Burichenko},
title = {Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3${,~II}},
journal = {Trudy Instituta matematiki},
pages = {101--111},
year = {2023},
volume = {31},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a11/}
}
TY - JOUR
AU - V. P. Burichenko
TI - Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3$, II
JO - Trudy Instituta matematiki
PY - 2023
SP - 101
EP - 111
VL - 31
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UR - http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a11/
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%0 Journal Article
%A V. P. Burichenko
%T Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3$, II
%J Trudy Instituta matematiki
%D 2023
%P 101-111
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a11/
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%F TIMB_2023_31_1_a11
It is proved that there is no algorithm for multiplication of $3\times 3$ matrices of multiplicative length $\leqslant 23$ that is invariant under a certain group isomorphic to $S_4\times S_3$. The proof uses description of the orbits of this group on decomposable tensors in the tensor cube $(M_3(\mathbb{C}))^{\otimes 3}$ which was obtained earlier.
[1] V. P. Burichenko, “Non-existence of a short algorithm for multiplication of $3\times 3$ matrices with group $S_x\times S_3$”, Tr. In-ta matematiki [Proceedings of the Institute of mathematics], 30:1-2 (2022), 99–116
[2] V. P. Burichenko, Symmetries of matrix multiplication algorithms. I, 2015, arXiv: 1508.01110 | Zbl
[3] V. P. Burichenko, “The isotropy group of the matrix multiplication tensor”, Tr. In-ta matematiki [Proceedings of the Institute of mathematics], 24:2 (2016), 106–118 | MR
