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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On Paravectors and Their Associated Algebras

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Vaz, Jr., Jayme
Total Authors: 1
Document type: Journal article
Source: Advances in Applied Clifford Algebras; v. 29, n. 2 APR 2019.
Web of Science Citations: 0

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