Cayley-Dickson Construction
Artur Korniłowicz
Formalized Mathematics, Tome 20 (2012), p. 281-290 / Harvested from The Polish Digital Mathematics Library

Cayley-Dickson construction produces a sequence of normed algebras over real numbers. Its consequent applications result in complex numbers, quaternions, octonions, etc. In this paper we formalize the construction and prove its basic properties.

Publié le : 2012-01-01
EUDML-ID : urn:eudml:doc:268274
@article{bwmeta1.element.doi-10_2478_v10037-012-0034-9,
     author = {Artur Korni\l owicz},
     title = {Cayley-Dickson Construction},
     journal = {Formalized Mathematics},
     volume = {20},
     year = {2012},
     pages = {281-290},
     zbl = {1288.17002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0034-9}
}
Artur Korniłowicz. Cayley-Dickson Construction. Formalized Mathematics, Tome 20 (2012) pp. 281-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0034-9/

[1] Grzegorz Bancerek. K¨onig’s theorem. Formalized Mathematics, 1(3):589-593, 1990.

[2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[3] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.

[4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

[5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

[8] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

[9] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.

[10] Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991.

[11] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.

[12] Michał Muzalewski and Wojciech Skaba. From loops to abelian multiplicative groups with zero. Formalized Mathematics, 1(5):833-840, 1990.

[13] Henryk Oryszczyszyn and Krzysztof Prazmowski. Real functions spaces. FormalizedMathematics, 1(3):555-561, 1990. | Zbl 0916.51004

[14] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.

[15] Yasunari Shidama. The Banach algebra of bounded linear operators. Formalized Mathematics, 12(2):103-108, 2004.

[16] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.

[17] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.

[18] Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers. FormalizedMathematics, 1(3):445-449, 1990.

[19] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.

[20] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.

[21] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[22] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.

[23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.