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Universal R-Matrix for Esoteric Quantum Groups

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Abstract

The universal R-matrix for a class of esoteric (nonstandard) quantum groups \(\mathcal{U}\)q(gl(2N+1)) is constructed as a twisting of the universal R-matrix \(\mathcal{R}\)S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle \(\mathcal{F}\) is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's \(\mathcal{B}\)(N)⊂\(\mathcal{U}\)q (gl(2N+1))), providing the factorization property of \(\mathcal{F}\) . As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo.

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Authors
  1. P.P. Kulish
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  2. A.I. Mudrov
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Kulish, P., Mudrov, A. Universal R-Matrix for Esoteric Quantum Groups. Letters in Mathematical Physics 47, 139–148 (1999). https://doi.org/10.1023/A:1007538903995

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