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Jordan algebras arising in population genetics

Published online by Cambridge University Press:  20 January 2009

P. Holgate
P. Holgate
Affiliation:
Department of Statistics, Birkbeck College, London, W.C.1
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The non-associative algebras arising in genetics (1), are rather isolated from other branches of non-associative algebra (6). However, in a paper (5), in which he studied these algebras in terms of their transformation algebras, Schafer proved that the gametic and zygotic algebras for a single diploid locus are Jordan algebras.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 4 , December 1967 , pp. 291 - 294
Copyright
Copyright © Edinburgh Mathematical Society 1967

References

REFERENCES

(1) Etherington, I. M. H., Genetic algebras, Proc. Roy. Soc. Edinburgh, 59 (1939), 242–258.CrossRefGoogle Scholar
(2) Etherington, I. M. H., Duplication of linear algebras, Proc. Edinburgh Math. Soc. (2), 6 (1941), 222–230.CrossRefGoogle Scholar
(3) Gonshor, H., Special train algebras arising in genetics, Proc. Edinburgh Math. Soc. (2), 12 (1960), 41–53.CrossRefGoogle Scholar
(4) Paige, L. J., Jordan algebras, in Studies in Modern Algebra, ed.Albert, A. A. (Math. Assn. of America, 1963).Google Scholar
(5) Schafer, R. D., Structure of genetic algebras, Amer. J. Math. 71 (1949), 121–135.CrossRefGoogle Scholar
(6) Schafer, R. D., Structure and representation of non-associative algebras, Bull. Amer. Math. Soc. 61 (1955), 469–484.CrossRefGoogle Scholar