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Clifford algebras and isotropes

Published online by Cambridge University Press:  18 May 2009

P. L. Robinson
P. L. Robinson*
Affiliation:
Department Of Mathematics, University College Dublin, Belfield, Dublin 4
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Isotropes play a distinguished rôle in the algebra of spinors. Let V be an even-dimensional real vector space equipped with an inner product Bof arbitrary signature. An isotrope of (V, B) is a subspace of the complexification Vc on which Bc is identically zero. Denote by ρ the spin representation of the complex Clifford algebra C(Vc, Bc) on a space S of spinors.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 2 , July 1987 , pp. 249 - 257
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

1 Atiyah, M. F., Bott, R. and Shapiro, A., Clifford modules, Topology 3 (1964), Suppl. 1, 3–38.CrossRefGoogle Scholar
2 Chevalley, C., The algebraic theory of spinors (Columbia University Press, 1954).CrossRefGoogle Scholar
3 Chevalley, C., The construction and study of certain important algebras (The Mathematical Society of Japan, 1955).Google Scholar
4 Greub, W., Multilinear algebra, second edition (Springer, 1978).CrossRefGoogle Scholar
5 Robinson, P. L., Mpc structures and applications (Doctoral thesis, University of Warwick, 1984).Google Scholar