QUANTUM INVARIANCE GROUPS OF PARTICLE ALGEBRAS

Part of the NATO Science Series book series (NAII, volume 201)

Abstract

The boson and fermion algebras as well as their various generalizations posess invariance under quantum groups. One example is FIO (2d, R), the fermionic inhomogenous orthogonal quantum group which is the inhomogenous quantum invariance group of the d-dimensional fermion algebra. Another is BISp(2d, R), the bosonic inhomogenous symplectic quantum group which is the inhomogenous quantum invariance group of the d-dimensional boson algebra. Complexification, sub(quantum) groups and quantum group manifolds of these quantum groups will also be discussed.

Keywords

Manifold Turkey 

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References

  1. 1.
    Fadeev, L. D., Reshetikhin, N. Y., and Takhtajan, L. A. (1987) Quantization of Lie groups and Lie algebras, Math. J., 1, p. 193.Google Scholar
  2. 2.
    Arik, M., Gün, S., and Yildiz, A. (2003) Invariance quantum group of the fermionic oscillator, Europ. Phys. J. C. 27, pp. 453–455.CrossRefADSGoogle Scholar
  3. 3.
    Arik, M. and Kayserilioğlu, U. (2003) Quantum invariance groups of bosons and fermions, hep-th/0304185.Google Scholar
  4. 4.
    Arik, M. and Baykal, A. (2003) Riemannian metric of the invariance group of the fermion algebra, Gen. Relat. Gravit. 35, pp. 885–890.MATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • M. Arik
    • 1
  1. 1.Department of PhysicsBoğaziçi UniversityIstanbulTurkey

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