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Quantum de rham complex with d3=0 differential

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Czechoslovak Journal of Physics Aims and scope

Abstract

In this work, we construct the de Rham complex with differential operator d satisfying theQ-Leibniz rule, whereQ is a complex number, and the condition d3=0 on an associative unital algebra with quadratic relations. Therefore we introduce the second order differentials d2 xi. In our formalism, besides the usual two-dimensional quantum plane, we observe that the second order differentials d2 x and d2 y generate either bosonic or fermionic quantum planes, depending on the choice of the differentiation parameterQ.

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References

  1. C. Chryssomalakos, P. Schupp, and B. Zumino: Alg. Anal.6 (1994) 252.

    MathSciNet  Google Scholar 

  2. B.L. Cherchiai, R. Henterding, J. Madore, and J. Wess: Eur. Phys. J.8 (1998) 547.

    Article  ADS  Google Scholar 

  3. R. Coquereaux and A.O. Garcia: Rev. Math. Phys.12 (2000) 227.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Kerner: inConf. ICGTMP “Group-23”, Dubna, Russia, July 30 – August 6, 2000, math-ph/0011023.

    Google Scholar 

  5. V. Abramov and R. Kerner: J. Math. Phys.41 (2000) 5598.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. R. Kerner: J. Math. Physics33 (1992) 403.

    Article  ADS  MathSciNet  Google Scholar 

  7. M. Dubois-Violette: K-theory14 (1998) 371.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Dubois-Violette: Czech. J. Phys.46 (1996) 1227; q-alg/9609012.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. M. Dubois-Violette and I.T. Todorov: Lett. Math. Phys.48 (1999) 323; hep-th/9704069.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Wess and B. Zumino: Nucl. Phys. B: Proc. Suppl.18 (1990) 302.

    Article  ADS  MathSciNet  Google Scholar 

  11. V. K. Kharchenko and A.Borowiec:Questions of algebra and logic, Trudy Inst. Mat. Im. S. L. Soboleva SO RAN, Novosibirsk, Vol. 30, 1996, p. 164 (in Russian).

  12. L. Hlavatý: J. Phys. A: Math. Gen.25 (1992) 485.

    Article  MATH  ADS  Google Scholar 

  13. W. Pusz and S. Woronowicz: Rep. Math. Phys.27 (1989) 231.

    Article  MATH  MathSciNet  Google Scholar 

  14. S.K. Soni: J. Phys. A: Math. Gen.24 (1991) 169.

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Pure Mathematics, University of Tartu, Vanemuise 46, 51014, Tartu, Estonia

    N. Bazunova

  2. Institute of Theoretical Physics, University of Wrocław, plac Maksa Borna 9, PL 50-204, Wrocław, Poland

    A. Borowiec

  3. Laboratoire de Physique Theorique des Liquides, Université Paris-VI, Tour 22, 4-ème étage, Boite 142, 4, Place Jussieu, 75005, Paris, France

    R. Kerner

Authors
  1. N. Bazunova
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  2. A. Borowiec
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  3. R. Kerner
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Additional information

R.K. thanks M. Dubois-Violette for constructive remarks, and C.Burdik for his help in arranging the manuscript. N.B. and A.B. wish to thank for hospitality the Laboratoire LPTL where this paper has been written.

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Bazunova, N., Borowiec, A. & Kerner, R. Quantum de rham complex with d3=0 differential. Czech J Phys 51, 1266–1271 (2001). https://doi.org/10.1023/A:1013301532095

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  • DOI: https://doi.org/10.1023/A:1013301532095

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