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Colour algebras and Cayley–Dickson algebras

Published online by Cambridge University Press:  14 November 2011

Alberto Elduque  and
Hyo Chul Myung
Alberto Elduque
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Hyo Chul Myung
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, Iowa 50614, U.S.A
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Abstract

Forms of the colour algebra introduced by Domokos and Kövesi-Domokos are studied by relating them to the well-known Cayley–Dickson algebras. Automorphisms groups and derivation algebras of these algebras are also determined.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 6 , 1995 , pp. 1287 - 1303
Copyright
Copyright © Royal Society of Edinburgh 1995

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References

1Bahturin, Yu. A., Mikhalev, A. A., Petrogradsky, V. M. and Zaicev, M. V.. Infinite Dimensional Lie Superalgebras (Berlin: Walter de Gruyter, 1992).CrossRefGoogle Scholar
2Domokos, G. and Kovesi-Domokos, S.. The algebra of color. J. Math. Phys. 19 (1978), 1477–81.CrossRefGoogle Scholar
3Elduque, A.. On the color algebra. Algebras Groups Geom. 5 (1988), 395–410.Google Scholar
4Elduque, A.. Derivaciones del álegebra de color. In Actas de las XIV Jornadas Hispano-Lusas de Matemáticas, Puerto de la Cruz, 1989, vol. I, 45–9 (Universidad de La Laguna: Secretariado de Publicaciones, 1989, in Spanish).Google Scholar
5Elduque, A. and Myung, H. C.. Color algebras and affine connections on S6. J. Alegbra 149 (1992), 234–61.CrossRefGoogle Scholar
6Elduque, A. and Myung, H. C.. Note on the Cayley algebra and connections on S6. In Hadronic Mechanics and Nonpotential Interactions, ed. Myung, H. C., 139–47 (New York: Nova Science, 1992).Google Scholar
7Elduque, A. and Myung, H. C.. The reductive pair (B3, G2) and affine connections on S7. J. Pure Appl. Algebra 86 (1993), 155–71.CrossRefGoogle Scholar
8Holmann, H.. Aufbau des Zahlsystems (Fernuniversität-Gesamthochschule in Hagen, 1983).Google Scholar
9Jacobson, N.. Composition algebras and their automorphisms. Rend. Circ. Mat. Palermo (2) 7 (1958), 55–80.CrossRefGoogle Scholar
10Jacobson, N.. Lie Algebras (New York: Interscience, 1962).Google Scholar
11Schafer, R. D.. An Introduction to Nonassociative Algebras (New York: Academic Press, 1966).Google Scholar
12Schafer, R. D.. A generalization of the algebra of color I. J. Algebra 160 (1993), 93–129.CrossRefGoogle Scholar
13Schafer, R. D.. A generalization of the algebra of colour II. J. Algebra 166 (1994), 296–309.CrossRefGoogle Scholar
14Shafer, R. D.. Noncommutative Jordan algebras satisfying ([x, y], y, y) = 0. J. Algebra 169 (1994), 194–9.CrossRefGoogle Scholar
15Shaw, R.. A 2-dimensional quaternionic construction of an 8-dimensional ternary composition algebra. Nuovo Cimento B 104 (1989), 163–76.CrossRefGoogle Scholar
16Zorn, M.. Theorie der alternativen ringen. Abh. Math. Sem. Univ. Hamburg 8 (1930), 123–47.CrossRefGoogle Scholar