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Diskretnaya Matematika, 1997, Volume 9, Issue 1, Pages 71–82
DOI: https://doi.org/10.4213/dm449 (Mi dm449) 		 
Minimal extensions with simple multiplication for an algebra of second-order matrices

V. B. Alekseev
Full-text PDF (983 kB)
DOI: https://doi.org/10.4213/dm449
Abstract: It is shown that the results of Strassen on existence of bilinear algorithm with seven multiplications for multiplication of matrices of order 2 has the following simple interpretation: there exists a 7-dimensional algebra with simple multiplication that is an extension of the algebra of matrices of order 2. It is proved that exactly three such 7-dimensional algebras exist.
This work was supported by the Russian Foundation for Basic Research, Grant 94-01-01206.
Received: 16.05.1994
Bibliographic databases:
UDC: 519.7
Language: Russian
Citation: V. B. Alekseev, “Minimal extensions with simple multiplication for an algebra of second-order matrices”, Diskr. Mat., 9:1 (1997), 71–82; Discrete Math. Appl., 7:1 (1997), 89–101
Citation in format AMSBIB
\Bibitem{Ale97}
\by V.~B.~Alekseev
\paper Minimal extensions with simple multiplication for an algebra of second-order matrices
\jour Diskr. Mat.
\yr 1997
\vol 9
\issue 1
\pages 71--82
\mathnet{http://mi.mathnet.ru/dm449}
\crossref{https://doi.org/10.4213/dm449}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1454180}
\zmath{https://zbmath.org/?q=an:0887.15011}
\transl
\jour Discrete Math. Appl.
\yr 1997
\vol 7
\issue 1
\pages 89--101
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