Skip to main content
SpringerLink
Log in

Differential algebra of quantum fermions

  • Published:
Czechoslovak Journal of Physics Aims and scope

Abstract

Lie coalgebra equips an exterior algebra (algebra of fermions) with a structure of a differential algebra. In similar way we equip an algebra of quantum fermions (quantized exterior algebra) with a structure of a differential algebra. This leads to a notion of a variety of Lie coalgebras for a Hecke braid. This approach is different from that of Gurevich (1988 and 1993), Woronowicz (1989) and of Majid (1993).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Claude C. and Eilenberg S.: Trans. AMS63 (1948) 85.

    Google Scholar 

  2. Koszul J.-L.: Bull. Soc. Math. France78 1.

  3. Mitra Bani and Tripathy K. C.: J. Math. Phys.25 (1984) 2550.

    Google Scholar 

  4. Eilenberg S.: Ann. Soc. Polon. Math.21 (1948) 125.

    Google Scholar 

  5. Gurevich D.: Soviet Math. Doklady33 (1986) 758.

    Google Scholar 

  6. Gurevich D.:in Spinors, Twistors, Clifford Algebras and Quantum Deformations.In series Fundamental Theories of Physics (edited by Z. Oziewicz, B. Jancewicz and A. Borowiec). Kluwer Academic Publishers, Dordrecht, 1993.

    Google Scholar 

  7. Woronowicz S. L.: Commun. Math. Phys.122 (1989) 125.

    Google Scholar 

  8. Majid S.: Quantum and braided Lie algebras, preprint DAMTP/93-4, 1993 (to appear in J. Geometry and Physics); Braided geometry: a new approach toq-deformations, preprint;in Advances in Applied Clifford Algebras, Vol. 4 (Proc. XXIIth Conf. on Differential Geometric Methods in Theoretical Physics, Ixtapa, Mexico, ed. by J. Keller), 1994 (to appear).

  9. Joyal A. and Street R.: Braided monoidal categories. Macquarie Mathematics Reports 850067 (1985) and 860081 (1986).

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

    Google Scholar 

  11. Scheunert M.: J. Math. Phys.20 (1979) 712.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wrocław, Plac Maxa Borna 9, 50204, Wrocław, Poland

    Zbigniew Oziewicz & Jerzy Różański

Authors
  1. Zbigniew Oziewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jerzy Różański
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported in part by Polish Committee for Scientific Research, KBN.

In 1994 at Centro de Investigaciones Teoricas, Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autonoma de México, Apartado Postal # 25, Cuautitlán Izcalli, 54700 Estado de México. E-mail: oziewicz@redvaxl.dgsca.unam.mx, oziewicz@plwruwll.bitnet

Rights and permissions

Reprints and permissions

About this article

Cite this article

Oziewicz, Z., Różański, J. Differential algebra of quantum fermions. Czech J Phys 44, 1081–1089 (1994). https://doi.org/10.1007/BF01690460

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01690460

Keywords

Search

Navigation