, Volume 93, Issue 2, pp 1292-1307

Poisson-Lie groups. The quantum duality principle and the twisted quantum double

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The quantum duality principle relates the quantum groups that arise on the quantization of Poisson-Lie dual groups and generalizes Fourier duality. Also considered are the theory of the Heisenberg double, which replaces the cotangent bundle for quantum groups, and its deformations (the twisted double).

St Petersburg Branch of the V. A. Steklov Mathematics Institute, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 93, No. 2, pp. 302–329, November, 1992.