Results 11 to 20 of about 12,285 (254)
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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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
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IEEE Access, 2023 The processing of color images is of great interest, because the human perception of color is a very complex process, still not well understood. In this article, firstly the authors present an analysis of the well-known mathematical methods used to model
Eduardo Bayro-Corrochano +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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Hamiltonian Mechanical System with Split Quaternions [PDF]
Universal Journal of Applied Mathematics, 2018 In this article, firstly we study about geometrical applications of split quaternions. Then, we obtain Hamitonian mechanical systems with Split quaternions. Quaternionic and Coquaternionic (split analoque of quaternions) extensions of Hamiltonian mechanics are introduced and are shown as offer a unifying framework for quantum mechanics.
Yormaz, Cansel +2 more
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Hyperkähler, bi-hypercomplex, generalized hyperkähler structures and T-duality
Nuclear Physics B, 2022 We exploit the doubled formalism to study comprehensive relations among T-duality, complex and bi-hermitian structures (J+,J−) in two-dimensional N=(2,2) sigma models with/without twisted chiral multiplets. The bi-hermitian structures (J+,J−) embedded in
Tetsuji Kimura +2 more
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Order 3 elements in G2 and idempotents in symmetric composition algebras [PDF]
, 2017 Order three elements in the exceptional groups of type G2 are classified up to conjugation over arbitrary fields. Their centralizers are computed, and the associated classification of idempotents in symmetric composition algebras is obtained. Idempotents
Elduque, Alberto
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Research on splitting quaternions with generalized Tribonacci hybrid number components [PDF]
Notes on Number Theory and Discrete MathematicsThis paper introduces the Generalized Tribonacci Hybrid Split Quaternion (GTHSQ), a novel split quaternion with coefficients derived from generalized Tribonacci hybrid numbers.
Yanni Yang, Yong Deng
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Quaternion algebras with the same subfields [PDF]
, 2009 G. Prasad and A. Rapinchuk asked if two quaternion division F -algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an extension of a global
A Merkurjev +9 more
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