P. Girard: Quaternion Grassmann-Hamilton-Clifford algebras

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Quaternion Grassmann-Hamilton-Clifford algebras: new mathematical tools for classical and relativistic modeling

by Patrick R. Girard (University of Lyon; Creatis; Insa-Lyon; France)
in O. Doessel and W.C. Schlegel (Eds.): WC 2009, IFMBE Proceedings 25/IV,
pp. 65-68, 2009. www.springerlink.com

Abstract
The paper presents new mathematical tools for classical and relativistic modeling based on a quaternion formulation of Clifford algebras which we shall call Grassmann-Hamilton-Clifford algebras. These algebras allow to develop an associative exterior calculus for any metric and any dimension yielding probably the best representations of the covariance groups. As applications, the paper develops these algebras in euclidean three-space and pseudo-euclidean spacetime, and in particular the Frenet frame and the relativistic moving frame.

Keywords
Quaternions, biquaternions, tetraquaternions, Grassmann-Hamilton-Clifford algebras, classical and relativistic modeling.

Source: Email by P. Girard (21 Oct. 2009), patrick.girard_at_insa-lyon.fr

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