Forms of Low Rank

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 294)


This chapter illustrates how the theory of Clifford algebras can be used for a systematic study of quadratic spaces of low rank. Results from Knus- Ojanguren-Sridharan [1978], Knus-Paques [1985], Knus [1988], Knus- Parimala-Sridharan [1989] and Knus-Parimala-Sridharan [1990] are given without explicit references. For forms of rank ≤6 we compute the invariants and discuss how far they determine the forms. If the rank is odd we usually consider semiregular forms, so that we also obtain results if 2 is not invertible.


Clifford Algebra Hermitian Form Quaternion Algebra Quadratic Space Quadratic Module 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  1. 1.Department MathematikETH-ZentrumZürichSwitzerland

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