# Statistics and quantum group symmetries

Banach Center Publications (1997)

- Volume: 40, Issue: 1, page 369-377
- ISSN: 0137-6934

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topFiore, Gaetano, and Schupp, Peter. "Statistics and quantum group symmetries." Banach Center Publications 40.1 (1997): 369-377. <http://eudml.org/doc/252192>.

@article{Fiore1997,

abstract = {Using 'twisted' realizations of the symmetric groups, we show that Bose and Fermi statistics are compatible with transformations generated by compact quantum groups of Drinfel'd type.},

author = {Fiore, Gaetano, Schupp, Peter},

journal = {Banach Center Publications},

keywords = {twisted transformations; Hopf algebra; quantum group transformations; quantum mechanics; Bose and Fermi statistics; compact quantum groups},

language = {eng},

number = {1},

pages = {369-377},

title = {Statistics and quantum group symmetries},

url = {http://eudml.org/doc/252192},

volume = {40},

year = {1997},

}

TY - JOUR

AU - Fiore, Gaetano

AU - Schupp, Peter

TI - Statistics and quantum group symmetries

JO - Banach Center Publications

PY - 1997

VL - 40

IS - 1

SP - 369

EP - 377

AB - Using 'twisted' realizations of the symmetric groups, we show that Bose and Fermi statistics are compatible with transformations generated by compact quantum groups of Drinfel'd type.

LA - eng

KW - twisted transformations; Hopf algebra; quantum group transformations; quantum mechanics; Bose and Fermi statistics; compact quantum groups

UR - http://eudml.org/doc/252192

ER -

## References

top- [1] W. Pusz, S. L. Woronowicz, Twisted Second Quantization, Reports on Mathematical Physics 27 (1989), 231-257. Zbl0707.47039
- [2] G. Fiore, P. Schupp, Identical Particles and Quantum Symmetries, Preprint LMU-TPW 95-10 (Munich University), hep-th 9508047, to appear in Nucl. Phys. B. Zbl1003.81504
- [3] V. G. Drinfeld, Quasi Hopf Algebras, Leningrad Math. J. 1 (1990), 1419.
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- [6] O. Ogievetsky, W. B. Schmidke, J. Wess and B. Zumino, q-Deformed Poincaré Algebra, Commun. Math. Phys. 150 (1992) 495-518.
- [7] S. Majid, Braided Momentum in the q-Poincaré Group, J. Math. Phys. 34 (1993), 2045. Zbl0786.17013
- [8] M. Pillin, W. B. Schmidke and J. Wess, q-Deformed Relativistic One-Particle States, Nucl. Phys. B403 (1993), 223.
- [9] G. Fiore, The Euclidean Hopf algebra ${U}_{q}\left({e}^{N}\right)$ and its fundamental Hilbert space representations, J. Math. Phys. 36 (1995), 4363-4405; The q-Euclidean algebra ${U}_{q}\left({e}^{N}\right)$ and the corresponding q-Euclidean lattice, Int. J. Mod. Phys. A, in press.
- [10] F. Bonechi, R. Giachetti, E. Sorace, M. Tarlini, Deformation Quantization of the Heisenberg Group, Commun. Math. Phys. 169 (1995), 627-633. Zbl0833.17017
- [11] R. Engeldinger, On the Drinfel'd-Kohno Equivalence of Groups and Quantum Groups, Preprint LMU-TPW 95-13.
- [12] T. L. Curtright, G. I. Ghandour, C. K. Zachos, Quantum Algebra Deforming Maps, Clebsh-Gordan Coefficients, Coproducts, U and R Matrices, J. Math. Phys. 32 (1991), 676-688. Zbl0749.17011

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