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A survey of some recent results on Clifford algebras in 4

Drahoslava Janovská, Gerhard Opfer (2023)

Applications of Mathematics

We will study applications of numerical methods in Clifford algebras in 4 , in particular in the skew field of quaternions, in the algebra of coquaternions and in the other nondivision algebras in 4 . In order to gain insight into the multidimensional case, we first consider linear equations in quaternions and coquaternions. Then we will search for zeros of one-sided (simple) quaternion polynomials. Three different classes of zeros can be distinguished. In general, the quaternionic coefficients can...

A tutorial on conformal groups

Ian Porteous (1996)

Banach Center Publications

Our concern is with the group of conformal transformations of a finite-dimensional real quadratic space of signature (p,q), that is one that is isomorphic to p , q , the real vector space p + q , furnished with the quadratic form x ( 2 ) = x · x = - x 1 2 - x 2 2 - . . . - x p 2 + x p + 1 2 + . . . + x p + q 2 , and especially with a description of this group that involves Clifford algebras.

Algebraic Connections and Curvature in Fibrations Bundles of Associative Algebras

Igor M. Burlakov (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this article fibrations of associative algebras on smooth manifolds are investigated. Sections of these fibrations are spinor, co spinor and vector fields with respect to a gauge group. Invariant differentiations are constructed and curvature and torsion of invariant differentiations are calculated.

Anisotropic complex structure on the pseudo-Euclidean Hurwitz pairs

W. Królikowski (1991)

Annales Polonici Mathematici

The concept of supercomplex structure is introduced in the pseudo-Euclidean Hurwitz pairs and its basic algebraic and geometric properties are described, e.g. a necessary and sufficient condition for the existence of such a structure is found.

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