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New quantum groups by double-bosonisation

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Czechoslovak Journal of Physics Aims and scope

Abstract

We obtain new family of quasitriangular Hopf algebras \(\mathbb{C}_q^{0|n} \rtimes U_q \widetilde{(su}_n ) \ltimes \mathbb{C}_q^{0|n}\) via the author's recent double-bosonisation construction for new quantum groups. They are versions of U q(su n+1) with a fermionic rather than bosonic quantum plane of roots adjoined to U q(su n). We give the n = 2 case in detail. We also consider the anyonic-double of an anyonic (\((\mathbb{Z}/n\mathbb{Z}{\text{ - graded)}}\)) braided group and the double-bosonisation of the free braided group in n variables.

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References

  1. Drinfeld V.G.: in Proc. Int. Congress of Mathematicians, Providence (R.I.) 1986 (Ed. A.M. Gleason), AMS, 1987, Vol. 1, p. 798.

  2. Majid S.: Isr. J. Math. 72 (1990) 133.

    Google Scholar 

  3. Faddeev L.D., Reshetikhin N.Yu., and Takhtajan L.A.: Leningrad Math. J. 1 (1990) 193.

    Google Scholar 

  4. Majid S.: Double bosonisation and the construction of U q(g). Preprints Damtp/95–57 + RIMS-1047, 1995.

  5. Majid S.: Braided geometry of the conformal algebra, J. Math. Phys. (to appear).

  6. Majid S.: Foundations of Quantum Group Theory. Cambridge University Press, 1995.

  7. Majid S.: in Quantum Groups, Integrable Statistical Models and Knot Theory (Editors M-L. Ge and H.J. de Vega), World Sci., Singapore, 1993, p. 231.

    Google Scholar 

  8. Majid S.: J. Algebra 163 (1994) 165.

    Google Scholar 

  9. Majid S.: Commun. Math. Phys. 156 (1993) 607.

    Google Scholar 

  10. Majid S.: Some comments on bosonisation and biproducts, Czech J. Phys. (1997) (to appear).

  11. Majid S. and Rodriguez-Plaza M.J.: J. Math. Phys. 36 (1995) 7071.

    Google Scholar 

  12. Majid S.: in Spinors, Twistors, Clifford Algebras and Quantum Deformations (Proc. 2nd Max Born Symposium, Wroclaw, Poland, 1992), (Eds. Z. Oziewicz et al.), Kluwer, Dordrecht, 1992, p. 327.

    Google Scholar 

  13. Majid S.: J. Math. Phys., 33 (1002) 3431.

    Google Scholar 

  14. Majid S.: J. Math. Phys. 34 (1993) 4843.

    Google Scholar 

  15. Lusztig G.: Introduction to Quantum Groups. Birkhauser, 1993.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Science Center, Cambridge, MA, 02138, USA

    S. Majid

  2. Department of Applied Mathematics & Theoretical Physics, University of Cambridge, Cambridge, CB3 9EW.

    S. Majid

  3. Royal Society University Research Fellow and Fellow of Pembroke College, Cambridge

    S. Majid

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  1. S. Majid
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Majid, S. New quantum groups by double-bosonisation. Czechoslovak Journal of Physics 47, 79–90 (1997). https://doi.org/10.1023/A:1021400329710

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  • DOI: https://doi.org/10.1023/A:1021400329710

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