On Paravectors and Their Associated Algebras

Author(s)

Vaz, Jr., Jayme

• Document type: Journal article
• Source: Advances in Applied Clifford Algebras; v. 29, n. 2 APR 2019.
• Web of Science Citations: 0

Abstract

Some algebraic structures that can be defined on the spaces of paravectors and k-paravectors are studied. Firstly, a version of the exterior and interior products resembling those in the exterior algebra of k-vectors but according to the k-paravector grading is defined. Secondly, a new Clifford algebra is constructed from the operations of exterior and interior products of paravectors and k-paravectors such that if the original vector space has a metric of signature (n,0), then the metric of this new Clifford algebras has a metric of signature (1,n). The noticeable difference between this new Clifford algebra and usual ones is the necessity of the conjugation operation in its definition. Thirdly, since the space of k-paravectors is not an invariant space under the Clifford product by a paravector, another product is defined in such a way to make the space of k-paravectors invariant under this product by a paravector. The algebra defined by this product is shown to be a DKP algebra. (AU)

• FAPESP's process: 16/21370-9 - Applications of Clifford Algebras in Computer Graphics
• Grantee: Jayme Vaz Junior
• Support Opportunities: Scholarships abroad - Research