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On the axiomatic foundations of the theory of Hermitian forms

Published online by Cambridge University Press:  24 October 2008

C. T. C. Wall
Affiliation:
University of Liverpool

Extract

In recent work on some topological problems (7), I was forced to adopt a complicated definition of ‘Hermitian form’ which differed from any in the literature. A recent paper by Tits(5) on quadratic forms over division rings contains a new and simple definition of these. A major objective of this paper is to formulate both these definitions in somewhat more general terms, and to show that they are equivalent.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Artin, E.Geometric algebra (Interscience, New York, 1957).Google Scholar
(2)Bass, H.Lectures on topics in algebraic K-theory (Tata Institute Bombay, 1967).Google Scholar
(3)Bourbaki, N. Algèbre ch. 9: Forines sesquilinéaires et formes quadratiques (Hermann, Paris, 1959).Google Scholar
(4)Dieudonné, J.La géométrie des groupes Classiques, 2nd ed. (Springer, Berlin, 1963).CrossRefGoogle Scholar
(5)Tits, J.Formes quadratiques, groupes orthogonaux, et algèbres do Clifford, Invent. Math. 5 (1968), 1941.CrossRefGoogle Scholar
(6)Wall, C. T. C.Quadratic forms on finite groups and related topics, Topology, 2 (1963), 281298.CrossRefGoogle Scholar
(7)Wall, C. T. C.Surgery of non simply-connected manifolds, Ann. of Math. 84 (1966), 217276.CrossRefGoogle Scholar
(8)Wall, C. T. C. Surgery of compact manifolds, to appear.Google Scholar