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DOI QR Code

COSET OF A HYPERCOMPLEX NUMBER SYSTEM IN CLIFFORD ANALYSIS

  • KIM, JI EUN ;
  • SHON, KWANG HO
  • Received : 2014.11.24
  • Published : 2015.09.30

Abstract

We give certain properties of elements in a coset group with hypercomplex numbers and research a monogenic function and a Clifford regular function with values in a coset group by defining differential operators. We give properties of those functions and a power of elements in a coset group with hypercomplex numbers.

Keywords

coset;differential operator;monogenic function;regular function;Clifford analysis

References

  1. D. C. Brody and E. M. Graefe, On complexified mechanics and coquaternions, J. Phys. A 44 (2011), no. 7, 072001, 9 pp.
  2. J. Dolbeault, M. J. Esteban, and E. Sere, On the eigenvalues of operators with gaps: Application to Dirac operators, J. Funct. Anal. 174 (2000), no. 1, 208-226. https://doi.org/10.1006/jfan.1999.3542
  3. K. Hasebe, Split-quaternionic Hopf map, quantum Hall effect, and twistor theory, Phys. Rev. D 81 (2010), no. 4, 041702, 5 pp.
  4. J. Hucks, Hyperbolic complex structures in physics, J. Math. Phys. 34 (1993), no. 12, 5986-6008. https://doi.org/10.1063/1.530244
  5. I. M. Jaglom, Complex Numbers in Geometry, Academic Press, New York, USA, 1968.
  6. J. E. Kim, S. J. Lim, and K. H. Shon, Taylor series of functions with values in dual quaternion, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 20 (2013), no. 4, 251-258.
  7. J. E. Kim, S. J. Lim, and K. H. Shon, Regular functions with values in ternary number system on the complex Clifford analysis, Abstr. Appl. Anal. 2013 (2013), Art. ID 136120, 7 pages.
  8. J. E. Kim, S. J. Lim, and K. H. Shon, Regularity of functions on the reduced quaternion field in Clifford analysis, Abstr. Appl. Anal. 2014 (2014), Art. ID 654798, 8 pages.
  9. J. E. Kim and K. H. Shon, The Regularity of functions on dual split quaternions in Clifford analysis, Abstr. Appl. Anal. 2014 (2014), Art. ID 369430, 8 pages.
  10. S. D. Leo, Quaternions and special relativity, J. Math. Phys. 37 (1996), no. 6, 2955-2968. https://doi.org/10.1063/1.531548
  11. H. I. Petrache, Coset group construction of multidimensional number systems, Symmetry 6 (2014), no. 3, 578-588. https://doi.org/10.3390/sym6030578
  12. G. Sobczyk, Geometric matrix algebra, Linear Algebra Appl. 429 (2008), no. 5, 1163-1173. https://doi.org/10.1016/j.laa.2007.06.015

Cited by

  1. PROPERTIES OF FUNCTIONS WITH VALUES IN FIBONACCI QUATERNIONS IN CLIFFORD ANALYSIS vol.38, pp.4, 2016, https://doi.org/10.5831/HMJ.2016.38.4.675
  2. PROPERTIES OF REGULAR FUNCTIONS WITH VALUES IN BICOMPLEX NUMBERS vol.53, pp.2, 2016, https://doi.org/10.4134/BKMS.2016.53.2.507
  3. DUAL QUATERNIONIC REGULAR FUNCTION OF DUAL QUATERNION VARIABLES vol.23, pp.1, 2016, https://doi.org/10.7468/jksmeb.2016.23.1.97
  4. THE DERIVATIVE OF A DUAL QUATERNIONIC FUNCTION WITH VALUES IN DUAL QUATERNIONS vol.37, pp.4, 2015, https://doi.org/10.5831/HMJ.2015.37.4.559

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)