Abstract
The first part of this chapter is mainly concerned with the construction of Clifford algebras for real and complex nondegenerate quadratic spaces of arbitrary rank and signature, these being presented as matrix algebras over ℝ, ℂ, ℍ, 2ℝ, 2ℂ or 2ℍ. In each case the algebra has an anti-involution known as conjugation, and the second part is concerned with determining products, or equivalently correlations, on the spinor space for which the induced adjoint anti-involution on the matrix algebra is conjugation. Applications of the classification are to the description of the Spin groups and conformal groups for quadratic spaces of low dimension.
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Porteous, I.R. (2004). Mathematical Structure of Clifford Algebras. In: Abłamowicz, R., Sobczyk, G. (eds) Lectures on Clifford (Geometric) Algebras and Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8190-6_2
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DOI: https://doi.org/10.1007/978-0-8176-8190-6_2
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