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We examine the properties of the quantum Lorentz group SO q(3, 1) using the [Formula: see text] matrix given in Ref. 14. We show that this matrix together with the q-deformed metric C provide a representation of a BWM algebra. Using the projection operators which decompose the [Formula: see text] matrix into irreducible components, we give the general definition of the corresponding quantum space, i.e. the q-deformed Minkowski space and the q-deformed Clifford algebra. We also construct the q analog of Dirac matrices and show that they form a matrix representation of the q-deformed Clifford algebra.

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