Canonical structure in SO(4)\(_ q\) and relations to E(3)\(_ q\) and SO(3,1)\(_ q\). (English) Zbl 0785.17012
The author constructs the \(q\)-algebra \(so_ q(4)\) starting with the quantum algebra \(su_ q(2)\otimes su_ q(2)\) and using Clebsch-Gordan coefficients of the algebra \(su_ q(2)\) (as the classical Lie algebra \(so(4)\) can be constructued from \(so(3)\otimes so(3)\)). Contraction to the \(q\)-algebra \(E_ q(3)\) and continuation to the “noncompact” \(q\)- algebra \(so_ q(3,1)\) are studied. The author constructs the structure of Hopf algebras in \(so_ q(4)\) and \(E_ q(3)\). Explicit formulas for the action of representation operators for these \(q\)-algebras are given. Let us note that there are other definitions of the \(q\)-algebra \(so_ q(4)\) which are not direct products of \(su_ q(2)\).
Reviewer: A.Klimyk (Kiev)
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
Keywords:
quantum algebra \(so_ q(4)\); contraction; continuation; Hopf algebras; action of representation operatorsReferences:
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