Geometric Roots of -1 in Clifford Algebras $\G_{p,q}$ with $p+q \leq 4$

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dc.creatorHitzer, Eckhard
dc.creatorAblamowicz, Rafal
dc.date2009-05-19
dc.date.accessioned2026-07-07T13:16:25Z
dc.date.available2026-07-07T13:16:25Z
dc.descriptionIt is known that Clifford (geometric) algebra offers a geometric interpretation for square roots of -1 in the form of blades that square to minus 1. This extends to a geometric interpretation of quaternions as the side face bivectors of a unit cube. Research has been done [S. J. Sangwine, Biquaternion (Complexified Quaternion) Roots of -1, Adv. Appl. Cliford Alg. 16(1), pp. 63-68, 2006.] on the biquaternion roots of -1, abandoning the restriction to blades. Biquaternions are isomorphic to the Clifford (geometric) algebra $Cl_{3}$ of $\R^3$. All these roots of -1 find immediate applications in the construction of new types of geometric Clifford Fourier transformations. We now extend this research to general algebras $Cl_{p,q}$. We fully derive the geometric roots of -1 for the Clifford (geometric) algebras with $p+q \leq 4$.
dc.description25 pages, detailed calculations, first presented at ICCA8, Las Campinas, Brazil
dc.identifierhttps://arxiv.org/abs/0905.3019
dc.identifierhttp://arxiv.org/abs/0905.3019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230785
dc.subjectRings and Algebras
dc.subjectComplex Variables
dc.subject15A66; 11E88; 42A38; 30G35
dc.titleGeometric Roots of -1 in Clifford Algebras $\G_{p,q}$ with $p+q \leq 4$
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