Tensor operators for quantum groups and applications. (English) Zbl 0747.17021
A general and coherent theory of tensor operators for Hopf algebras is given. Properties of tensor operators for a Lie algebra \(L\) or for its universal enveloping algebra \(U(L)\), and the natural Hopf algebra structure of \(U(L)\), are used to define tensor operators for general Hopf algebras. A main difference with \(U(L)\) is that in general a Hopf algebra need not be co-commutative, a property which is needed for the tensor product of tensor operators to be again a tensor operator. It is shown here that if the Hopf algebra has a universal \(R\) matrix (as is the case with quantum groups), then this difficulty can be overcome. As an application, some tensor operators for \(U_ q(sl(2))\) are constructed.
Reviewer: J.Van der Jeugt (Gent)
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 16W30 | Hopf algebras (associative rings and algebras) (MSC2000) |
Keywords:
tensor operators; Hopf algebras; universal \(R\) matrix; quantum groups; correlation functions; Heisenberg chainReferences:
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