Abstract
The non-commuting matrix elements of matrices from the quantum group GL q(2;C) with q = ω being the n-th root of unity are given a representation as operators in Hilbert space with help of C (n)4 generalized Clifford algebra generators.
The case of q ∈ C, |q| = 1 is treated parallelly.
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References
S. Vocos, B. Zumino, and J. Wess: Properties of Quantum 2×2 Matrices, LAPP-TH-253/89, June 1989.
L.D. Faddeev: Integrable models in (1+1)-dimensional quantum field theory, (Les Houches Lectures, 1982), Elsevier Science Publishers, Amsterdam, 1984.
L.D. Faddeev, N.Yu. Reshetikhin, and L.A. Takhatajan: Quantization of Lie groups and Lie algebras, LOMI preprint E-14-87 (see also in: M. Sato`s 60-th birthday volume).
Yu.I. Manin: Quantum Groups and Non-Commutative Geometry, Centre de Recherches Mathematiqes, University of Montreal, 1988. S.L. Woronowicz: Commun. Math. Phys. 111 (1987) 613.
E. Corrigan, D.B. Fairlie, P. Fletscher, and R. Sasaki: DTP-89/29, University of Durham, 1989.
M. Chaichian and D. Ellinas: J. Phys. A: Math. Gen. 23 (1990) 291. M. Rauch de Traubenberg: in Advances in Applied Clifford Algebras, Vol. 4 (2), 1994, p. 131.
A.K. Kwaśniewski: J. Math. Phys. 26 (1985) 2234.
Alain Connes and Marc A. Rieffel: Yang-Mills for Non-Commutative Two-Torri (Dedicated to Hans Borchers, Nico Hugenholtz, Richard V. Kadison and Daniel Kastler in Celebration of their Sixtieth Birthdays), American Mathematical Society, 1987.
A.K. Kwaśníewski, W. Bajguz, and I. Jaroszewski: in Advances in Applied Clifford Algebras, Vol. 8(2), 1998, p. 417.
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Kwaśniewski, A. Remarks on a representation of GL q (2;C) in terms of C (n)4 . Czechoslovak Journal of Physics 50, 123–127 (2000). https://doi.org/10.1023/A:1022837401591
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DOI: https://doi.org/10.1023/A:1022837401591