Displaying similar documents to “Hurwitz pairs and Clifford valued inner products”

Fischer decompositions in Euclidean and Hermitean Clifford analysis

Freddy Brackx, Hennie de Schepper, Vladimír Souček (2010)

Archivum Mathematicum

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Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator ∂ ̲ . In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator ∂ ̲ J , leading to the system of equations ∂ ̲ f = 0 = ∂ ̲ J f expressing so-called Hermitean monogenicity. The invariance...

Charge conjugation and Maiorana spinors in dimension 8

Pertti Lounesto (1996)

Banach Center Publications

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It is a common belief among theoretical physicists that the charge conjugation of the Dirac equation has an analogy in higher dimensional space-times so that in an 8-dimensional space-time there would also be Maiorana spinors as eigenspinors of a charge conjugation, which would swap the sign of the electric charge of the Dirac equation. This article shows that this mistaken belief is based on inadequate distinction between two kinds of charge conjugation: the electric conjugation swapping...

Discrete minimal surface algebras.

Arnlind, Joakim, Hoppe, Jens (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Supercomplex structures, surface soliton equations, and quasiconformal mappings

Julian Ławrynowicz, Katarzyna Kędzia, Osamu Suzuki (1991)

Annales Polonici Mathematici

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Hurwitz pairs and triples are discussed in connection with algebra, complex analysis, and field theory. The following results are obtained: (i) A field operator of Dirac type, which is called a Hurwitz operator, is introduced by use of a Hurwitz pair and its characterization is given (Theorem 1). (ii) A field equation of the elliptic Neveu-Schwarz model of superstring theory is obtained from the Hurwitz pair (⁴,³) (Theorem 2), and its counterpart connected with the Hurwitz triple ( 11 , 11 , 26 ) is...

Involution Matrix Algebras – Identities and Growth

Rashkova, Tsetska (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 16R50, 16R10. The paper is a survey on involutions (anti-automorphisms of order two) of different kinds. Starting with the first systematic investigations on involutions of central simple algebras due to Albert the author emphasizes on their basic properties, the conditions on their existence and their correspondence with structural characteristics of the algebras. Focusing on matrix algebras a complete description of involutions of...

Determinant evaluations for binary circulant matrices

Christos Kravvaritis (2014)

Special Matrices

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Determinant formulas for special binary circulant matrices are derived and a new open problem regarding the possible determinant values of these specific circulant matrices is stated. The ideas used for the proofs can be utilized to obtain more determinant formulas for other binary circulant matrices, too. The superiority of the proposed approach over the standard method for calculating the determinant of a general circulant matrix is demonstrated.