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Transitivity in integral symplectic forms

Published online by Cambridge University Press:  09 April 2009

D. G. James
D. G. James
Affiliation:
The Pennsylvania State University
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A Symplectic lattice L is a free Z-module of finite rank endowed with a non-degenerate alternating bilinear form. Thus we have a bilinear mapping Φ of L × L into the domain of integers Z; we donote Φ (α, β) by α · β (where α, β ∈ L). Then α2 = 0 and α·β = −β·α.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 1 , February 1968 , pp. 43 - 48
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Bourbaki, N., Algèbre, Ch. 9 (Hermann, Paris, 1959).Google Scholar
[2]James, D. G., ‘Integral invariants for vectors over local fields’, Pac. J. Math. 15 (1965), 905–916.CrossRefGoogle Scholar
[3]Kneser, M., ‘Darstellungsmasse indefiniter quadratischer Formen’, Math. Z. 77 (1961), 188–194.CrossRefGoogle Scholar
[4]Riehm, Carl R., ‘The structure of the symplectic group over a valuation ring’, Amer. J. Math. 88 (1966), 106–128.CrossRefGoogle Scholar
[5]Wall, C. T. C., ‘On the orthogonal group of unimodular quadratic forms’, Math. Ann. 147 (1962), 328–338.CrossRefGoogle Scholar