Geodesic
Minimal extensions with simple multiplication for an algebra of second-order matrices
Diskretnaya Matematika, Tome 9 (1997) no. 1, pp. 71-82.

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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. 
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     author = {V. B. Alekseev},
     title = {Minimal extensions with simple multiplication for an algebra of second-order matrices},
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V. B. Alekseev. Minimal extensions with simple multiplication for an algebra of second-order matrices. Diskretnaya Matematika, Tome 9 (1997) no. 1, pp. 71-82. http://geodesic.mathdoc.fr/item/DM_1997_9_1_a5/