Abstract
The two-dimensional Euclidean quantum algebra is considered at roots of unity. The algebraic properties and the Poisson-Hopf structure are first investigated. We then determine the irreducible representations and study the reduction of the tensor product of two of them.
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References
Vaksman, L. L. and Korogodski, L. I.,Soviet Math. Dokl. 39, 173 (1989).
Celeghini, E., Giachetti, R., Sorace, E., and Tarlini M.,J. Math. Phys. 31, 2548 (1990) and Contractions of quantum groups, inLecture Notes in Mathematics 1510, Springer-Verlag, Berlin, 1992, p. 221.
Woronowicz, S. L.,Lett. Math. Phys. 23, 251 (1991);Comm. Math. Phys. 144, 417 (1992);Comm. Math. Phys. 149, 637 (1992).
Ballesteros, A., Celeghini, E., Giachetti, R., Sorace, E., and Tarlini, M.,J. Phys. A: Math. Gen. 26, 7495 (1993).
Bonechi, F., Celeghini, E., Giachetti, R., Pereña, C. M., Sorace, E., and Tarlini, M.,J. Phys. A: Math. Gen., in press, 1994.
De Concini, C. and Kac, V. G., Representations of quantum groups at roots of 1, inProgr. Math. 92, Birkhäuser, Boston, Mass. 1990, p. 471.
De Concini, C., Kac, V. G., and Procesi, C.,Comm. Math. Phys. 157, 405 (1993).
Lusztig, G.,Geom. Dedicata 35, 89 (1990).
Reshetikhin, N. Y. and Turaev, V. G.,Inv. Math. 103, 547 (1991).
Kirby, R. and Melvin, P.,Inv. Math. 105, 473 (1991).
Roche, P. and Arnaudon, D.,Lett. Math. Phys. 17, 295 (1989).
Chari, V. and Pressley, A.,Lett. Math. Phys. 26, 133 (1992).
Arnaudon, D.,Comm. Math. Phys. 159, 175 (1994).
McConnell, J. C. and Robson, J. C.,Noncommutative Noetherian Rings, Wiley, New York, 1987.