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What is a Bivector? | SpringerLink

Bivectors do not exist in Clifford algebras over arbitrary fields, especially they do not exist in a canonical way in char 2. However, there is a natural way to introduce bivectors in all other char 2, whilst the polarization formula gives a one to one correspondence between quadratic forms and symmetric bilinear forms. This paper reviews Chevalley’s construction for a quadratic form Q, and arbitrary, not necessarily symmetric, bilinear forms such that B(x,x) = Q(x). The exterior product is obtained from the Clifford product by Riesz’s formula x ⋀ u = 1/2 (x u + (−1)^k u x), where x ∊ V and u ∊ ⋀ ^k V.

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1. Institute of Mathematics, Helsinki University of Technology, SF-02150, Espoo, Finland

   Pertti Lounesto

1. Institute of Theoretical Physics, University of Wrocław, Wrocław, Poland

   Zbigniew Oziewicz , Bernard Jancewicz  & Andrzej Borowiec ,  & 

© 1993 Springer Science+Business Media Dordrecht

Lounesto, P. (1993). What is a Bivector?. In: Oziewicz, Z., Jancewicz, B., Borowiec, A. (eds) Spinors, Twistors, Clifford Algebras and Quantum Deformations. Fundamental Theories of Physics, vol 52. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1719-7_18

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• DOI: https://doi.org/10.1007/978-94-011-1719-7_18

• Publisher Name: Springer, Dordrecht

• Print ISBN: 978-94-010-4753-1

• Online ISBN: 978-94-011-1719-7

• eBook Packages: Springer Book Archive

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