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On the group of automorphisms of a Hopf map

Published online by Cambridge University Press:  22 January 2016

Takashi Ono
Takashi Ono*
Affiliation:
The Johns Hopkins University
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Let K be an infinite field of characteristic not 2. Let qx, qY be nonsingular quadratic forms on vector spaces X, Y over K, respectively. Assume that there is a bilinear map B:X × Y → Y such that qY(B(x, y)) = qx(x)qY(y). To each such triple {qx, qY, B} one associates the Hopf map h: Z = X × Y → W = K × Y by h(z) = (qx(x) – qY(y), 2B(x, y)), z = (x, y).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 79 , October 1980 , pp. 131 - 140
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

[ 1 ] Schafer, R., An introduction to nonassociative algebras, Academic Press, New York, 1966.Google Scholar
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[ 3 ] Kneser, M., Lectures on Galois cohomology of classical groups, Tata Institute, Bombay, 1969.Google Scholar
[ 4 ] Ono, T., On the Tamagawa number of algebraic tori, Ann. of Math. 78 (1963), 47–73.CrossRefGoogle Scholar