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Some Matrix Representations of Fibonacci Quaternions and Octonions

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An Erratum to this article was published on 29 May 2017

Abstract

In this study, starting with the usual definition of octonions, we introduce some matrix representations for Fibonacci quaternions and octonions. Then we give Cassini identity for Fibonacci octonions via matrices. Furthermore, we consider some fundamental properties of these algebraic structures.

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References

  1. Daboul J., Delbourgo R.: Matrix representation of octonions and generalizations. J. Math. Phys. 40(8), 4134–4150 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Flaut C., Shpakivskyi V.: Real matrix representations for the complex quaternions. Adv. Appl. Clifford Algebras 23(3), 657–671 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Halici S., Shpakivskyi V.: On complex Fibonacci quaternions. Adv. Appl. Clifford Algebras 23(1), 105–112 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Halici S., Shpakivskyi V.: On dual Fibonacci octonions. Adv. Appl. Clifford Algebras 25(4), 905–914 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kecilioglu O., Akkus I.: The Fibonacci octonions. Adv. Appl. Clifford Algebras 25(1), 151–158 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Koshy T.: Fibonacci and Lucas Numbers with Applications, vol. 51. Wiley, Hoboken (2011)

    Google Scholar 

  7. Lounesto P.: Clifford Algebras and Spinors, vol. 286. Cambridge university press, Cambridge (2001)

    Book  MATH  Google Scholar 

  8. Smith J.D.H.: An Introduction to Quasigroups and Their Representations. CRC Press, Boca Raton (2006)

    Book  Google Scholar 

  9. Turner, J.C., Shannon, A.G.: Introduction to a Fibonacci geometry. In: Bergum, G.E., et al., (eds.) Applications of Fibonacci Numbers, vol. 7, pp. 435–448. Kluwer Academic Publishers, Netherlands (1998)

  10. Wells A., Shpakivskyi V.: Moufang loops arising from Zorn vector matrix algebras. Comment. Math. Univ. Carolin. 51(2), 371–388 (2010)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

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

    Serpil Halici & Adnan Karataş

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  1. Serpil Halici
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  2. Adnan Karataş
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Correspondence to Serpil Halici.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s00006-017-0792-0.

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Halici, S., Karataş, A. Some Matrix Representations of Fibonacci Quaternions and Octonions. Adv. Appl. Clifford Algebras 27, 1233–1242 (2017). https://doi.org/10.1007/s00006-016-0661-2

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  • DOI: https://doi.org/10.1007/s00006-016-0661-2

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