On Clifford Algebras of a Bilinear Form with an Antisymmetric Part

Rafał Abłamowicz () and Pertti Lounesto ()
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Rafał Abłamowicz: Gannon University, Department of Mathematics
Pertti Lounesto: Helsinki University of Technology, Institute of Mathematics

A chapter in Clifford Algebras with Numeric and Symbolic Computations, 1996, pp 167-188 from Springer

Abstract: Abstract We explicitly demonstrate with a help of a computer that Clifford algebra Cℓ(B) of a bilinear form B with a non-trivial antisymmetric part A is isomorphic as an associative algebra to the Clifford algebra Cℓ(Q) of the quadratic form Q induced by the symmetric part of B [in characteristic ≠ 2], However, the multivector structure of Cℓ(B) depends on A and is therefore different than the one of Cℓ(Q). Operation of reversion is still an anti-automorphism of Cℓ(B). It preserves a new kind of gradation in ⋀ V determined by A but it does not preserve the gradation in ⋀ V. The demonstration is given for Clifford algebras in real and complex vector spaces of dimension ≤ 9 with a help of a Maple package ‘Clifford’. The package has been developed by one of the authors to facilitate computations in Clifford algebras of an arbitrary bilinear form B.

Keywords: Clifford algebra; contraction; exterior algebra; multilinear structure; reversion (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-8157-4_11

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DOI: 10.1007/978-1-4615-8157-4_11

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