Deformations of Multiparameter Quantum gl(N)

Details Deformations of Multiparameter Quantum gl(N) Deformations of Multiparameter Quantum gl(N)

1995-05-16

arxiv.org/abs/q-alg/9505016v1

Lett. Math. Phys. 34 (1995) 25

Mathematics

Quantum Algebra

15 pages. Plain TeX

Scientific paper

10.1007/BF00739372

Multiparameter quantum gl(N) is not a rigid structure. This paper defines an essential deformation as one that cannot be interpreted in terms of a similarity transformation, nor as a perturbation of the parameters. All the equivalence classes of first order essential deformations are found, as well as a class of exact deformations. This work provides quantization of all the classical Lie bialgebra structures (constant r-matrices) found by Belavin and Drinfeld for sl(n). A special case, that requires the Hecke parameter to be a cubic root of unity, stands out.

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