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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 215
Fusion of q-tensor operators: quasi-Hopf-algebraic pointof view A.G.Bytsko
Tensor operators associated with given quantum Lie algebra can be naturally described in R-matrix language. For this purpose one combines tensor operators of given weight in a matrix. The latter obeys certain exchange relation with the L-operators. Among such matrices there is a special one (we call it exact) whose rows are linearly independent tensor operators. It obeys additional relations involving, in particular, twisted R-matrix. We consider the fusion procedure for such exact matrices. The problem turns out to be equivalent to the problem of construction of the twisting element which appears in Drinfeld`s description of quasi-Hopf algebras. We give prescription for constructing of the twisted element in general situation and illustrate it by explicit calculations for the case of fundamental representation of the quantized sl(2) algebra.
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