dorsal/arxiv
View SchemaFusion of q-tensor operators: quasi-Hopf-algebraic point of view
| Authors | Andrei G. Bytsko |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9609007 |
| URL | https://arxiv.org/abs/q-alg/9609007 |
| Journal | Zap.Nauchn.Semin. POMI 245 (1997) 107-129; J.Math.Sciences 100 (2000) 2077-2091 (Engl. transl.) |
Abstract
Tensor operators associated with a given quantum Lie algebra admit a natural description in the R-matrix language. Here we employ the R-matrix approach to discuss the problem of fusion of tensor operators. The most interesting case is provided by the quantum WZNW model, where, by construction, we deal with sets of linearly independent tensor operators. In this case the fusion problem is equivalent to construction of an analogue F(p) of the twisting element F which is employed in Drinfeld's description of quasi-Hopf algebras. We discuss the construction of the twisting element F(p) in a general situation and give illustrating calculations for the case of the fundamental representation of U_q(sl(2)).
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"abstract": "Tensor operators associated with a given quantum Lie algebra admit a natural\ndescription in the R-matrix language. Here we employ the R-matrix approach to\ndiscuss the problem of fusion of tensor operators. The most interesting case is\nprovided by the quantum WZNW model, where, by construction, we deal with sets\nof linearly independent tensor operators. In this case the fusion problem is\nequivalent to construction of an analogue F(p) of the twisting element F which\nis employed in Drinfeld\u0027s description of quasi-Hopf algebras. We discuss the\nconstruction of the twisting element F(p) in a general situation and give\nillustrating calculations for the case of the fundamental representation of\nU_q(sl(2)).",
"arxiv_id": "q-alg/9609007",
"authors": [
"Andrei G. Bytsko"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"journal_ref": "Zap.Nauchn.Semin. POMI 245 (1997) 107-129; J.Math.Sciences 100\n (2000) 2077-2091 (Engl. transl.)",
"title": "Fusion of q-tensor operators: quasi-Hopf-algebraic point of view",
"url": "https://arxiv.org/abs/q-alg/9609007"
},
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