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On the quantum Lorentz group. (English) Zbl 1145.81382
Summary: The quantum analog of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indices we construct a quantum Minkowski metric. In this framework we show explicitly the correspondence between the \(\text{SL}(2,\mathbb C)\) and Lorentz quantum groups. Five Image matrices of the quantum Lorentz group are constructed in terms of the R matrix of \(\text{SL}(2,\mathbb C)\) group. These Image matrices satisfy Yang-Baxter equations and two of which have adequate properties tied to the quantum Minkowski space structure as the reality conditions of the coordinates and the symmetrization of the metric. It is also shown that the Minkowski metric leads to invariant and central lengths of four-vectors.
MSC:
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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