Mathematical Structure of Clifford Algebras

Ian R. Porteous ()
Additional contact information
Ian R. Porteous: University of Liverpool, Department of Mathematical Sciences, Division of Pure Mathematics

Chapter 2 in Lectures on Clifford (Geometric) Algebras and Applications, 2004, pp 31-52 from Springer

Abstract: 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.

Keywords: 15A66; 17B37; 20C30; 81R25; Clifford algebra; spinor; Radon-Hurwitz number; correlation; conjugation; conformal transformation; Vahlen matrix (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8190-6_2

Ordering information: This item can be ordered from
http://www.springer.com/9780817681906

DOI: 10.1007/978-0-8176-8190-6_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().