Geodesic
On some algebras associated with fast algorithms
Diskretnaya Matematika, Tome 8 (1996) no. 1, pp. 52-64 
V. B. Alekseev. On some algebras associated with fast algorithms. Diskretnaya Matematika, Tome 8 (1996) no. 1, pp. 52-64. http://geodesic.mathdoc.fr/item/DM_1996_8_1_a2/
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     author = {V. B. Alekseev},
     title = {On some algebras associated with fast algorithms},
     journal = {Diskretnaya Matematika},
     pages = {52--64},
     year = {1996},
     volume = {8},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1996_8_1_a2/}
}
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This paper shows that the results on the existence of fast bilinear algorithms for multiplication of complex numbers and quaternions can be interpreted as enclosure of these algebras into algebras of the corresponding dimensions with a simple multiplication table. The possibilities of such extensions for the complex numbers are completely investigated.This work was supported by the Russian Foundation for Basic Research, Grant 94–01–01206a.