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A Witt Theorem for Non-Defective Lattices

Published online by Cambridge University Press:  20 November 2018

Karl A. Morin-Strom
Karl A. Morin-Strom*
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts; McGill University, Montreal, Quebec
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In [10], Witt laid the foundation for the study of quadratic forms over fields. Suppose Q is a quadratic form defined on a finite dimensional vector space V over a field of characteristic not equal to 2. Witt showed that non-zero vectors x and y in V satisfying Q(x) = Q(y) can be mapped into each other via an isometry of the vector space V. More generally, if τ : W ⟶ W’ is an isometry between subspaces of V, then τ extends to an isometry ϕ of V.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 3 , 01 June 1978 , pp. 499 - 511
Copyright
Copyright © Canadian Mathematical Society 1978

References

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