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Split Fibonacci Quaternions

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Abstract

Starting from ideas given by Horadam in [5] , in this paper, we will define the split Fibonacci quaternion, the split Lucas quaternion and the split generalized Fibonacci quaternion. We used the well-known identities related to the Fibonacci and Lucas numbers to obtain the relations between the split Fibonacci, split Lucas and the split generalized Fibonacci quaternions. Moreover, we give Binet formulas and Cassini identities for these quaternions.

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Authors and Affiliations

  1. Faculty of Arts and Sciences, Department of Mathematics, Sakarya University, Sakarya, Turkey

    Mahmut Akyiğit, Hidayet Hüda Kösal & Murat Tosun

Authors
  1. Mahmut Akyiğit
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  2. Hidayet Hüda Kösal
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  3. Murat Tosun
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Correspondence to Mahmut Akyiğit.

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This work was completed with the support of our \({{\rm T{_E}X}}\) -pert.

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Akyiğit, M., Kösal, H.H. & Tosun, M. Split Fibonacci Quaternions. Adv. Appl. Clifford Algebras 23, 535–545 (2013). https://doi.org/10.1007/s00006-013-0401-9

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  • DOI: https://doi.org/10.1007/s00006-013-0401-9

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