# Einstein’s equations and Clifford algebra

@article{Girard1999EinsteinsEA, title={Einstein’s equations and Clifford algebra}, author={P. Girard}, journal={Advances in Applied Clifford Algebras}, year={1999}, volume={9}, pages={225-230} }

Einstein’s equations of the general theory of relativity are rewritten within a Clifford algebra. This algebra is otherwise isomorphic to a direct product of two quaternion algebras. A multivector calculus is developed within this Clifford algebra which differs from the corresponding complexified algebra used in the standard spacetime algebra approach.

#### 10 Citations

Quaternions, Clifford Algebra and Symmetry Groups

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This presentation focuses on the close link of Clifford algebras with quaternions which seems to have been neglected in recent developments [1-3]. A multivector calculus is presented within a… Expand

Einstein Metrics Induced by Natural Riemann Extensions

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Clifford algebras are used in theoretical physics and in particular, in the general theory of relativity, where Einstein’s equations are rewritten in Girard (Adv Appl Clifford Algebras 9(2):225–230,… Expand

Differential Geometry Revisited by Biquaternion Clifford Algebra

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The paper develops, in 3D Euclidean space, a biquaternion calculus, having an associative exterior product, and applies it to differential geometry, the formalism being new, the approach is intended to be pedagogical. Expand

Hyperquaternions: An Efficient Mathematical Formalism for Geometry

- Mathematics, Computer Science
- GSI
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A hyperquaternion formulation of pseudo-euclidean rotations and the Poincare groups in n dimensions and a canonical decomposition of these groups is developed as an extension of an euclidean formalism and illustrated by a 5D example. Expand

Dual Hyperquaternion Poincaré Groups

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A new representation of the Poincare groups in n dimensions via dual hyperquaternions is developed, hyperquaternions being defined as a tensor product of quaternion algebras (or a subalgebra… Expand

Hyperquaternions: A New Tool for Physics

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- 2018

A hyperquaternion formulation of Clifford algebras in n dimensions is presented. The hyperquaternion algebra is defined as a tensor product of quaternion algebras $$\mathbb {H}$$H (or a subalgebra… Expand

Certain nonlinear functions acting on the vector space H^n over the Quaternions H

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In this paper, we consider a certain type of nonlinear functions acting on a finite-dimensional vector space Hn over the ring H of all quaternions, for n ∈ N. Our main results show that: (i) every… Expand

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Quaternion Diffusion for Color Image Filtering

- Computer Science
- Journal of Computer Science and Technology
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A new method of color diffusion considering the direct interactions between color channel pairs is presented, which is based on quaternion diffusion (QD) equation, and the solution to linear QD and its analysis is shown. Expand

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