Results 11 to 20 of about 8,275 (244)
Split-Quaternions and the Dirac Equation [PDF]
Advances in Applied Clifford Algebras, 2014 We show that Dirac 4-spinors admit an entirely equivalent formulation in terms of 2-spinors defined over the split-quaternions. In this formalism, a Lorentz transformation is represented as a $2 \times 2$ unitary matrix over the split-quaternions. The corresponding Dirac equation is then derived in terms of these 2-spinors.
Guangbin Ren, Lin Chen, Haiyan Wang
exaly +11 more sources
On the Consimilarity of Split Quaternions and Split Quaternion Matrices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In his regard, we examine the solvability conditions and general solutions of the equations and in split quaternions and split quaternion ...
Kösal Hidayet Hüda +2 more
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Quaternionic Serret-Frenet Frames for Fuzzy Split Quaternion Numbers [PDF]
Advances in Fuzzy Systems, 2018 We build the concept of fuzzy split quaternion numbers of a natural extension of fuzzy real numbers in this study. Then, we give some differential geometric properties of this fuzzy quaternion.
Cansel Yormaz +2 more
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The Second Order Pole over Split Quaternions
Journal of Physics: Conference Series, 2014 This is an addition to a series of papers [FL1, FL2, FL3, FL4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra.
Libine, Matvei
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Split quaternion matrices [PDF]
Miskolc Mathematical Notes, 2012 In this paper, we consider split quaternions and split quaternion matrices. Firstly, we give some properties of split quaternions. After that we investigate split quaternion matrices using properties of complex matrices. Then we define the complex adjoint matrix of split quaternion matrices and we describe some of their properties. Furthermore, we give
Alagöz, Yasemin +2 more
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Journal of Science and Arts, 2021 In this study we introduce q-deformed split quaternions, that is, this deformation reduces to classical split quaternions as q->1 where q is a real parameter. It is also shown that there is a quantum group associated with q-deformed split quaternions, which is isomorphic to SUq(1,1).
ÖZAVŞAR, Muttalip +1 more
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Quadratic Split Quaternion Polynomials: Factorization and Geometry. [PDF]
Adv Appl Clifford Algebr, 2020 AbstractWe investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split quaternions.
Scharler DF, Siegele J, Schröcker HP.
europepmc +6 more sources
Complex structures, T-duality and worldsheet instantons in Born sigma models
Journal of High Energy Physics, 2022 We investigate doubled (generalized) complex structures in 2D-dimensional Born geometries where T-duality symmetry is manifestly realized. We show that Kähler, hyperkähler, bi-hermitian and bi-hypercomplex structures of spacetime are implemented in Born ...
Tetsuji Kimura +2 more
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Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras
Nonlinear Analysis, 2022 The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra.
Adolfas Dargys, Artūras Acus
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Sextonians and the magic square [PDF]
, 2004 Associated to any complex simple Lie algebra is a non-reductive complex Lie algebra which we call the intermediate Lie algebra. We propose that these algebras can be included in both the magic square and the magic triangle to give an additional row and ...
Westbury, Bruce
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