Quantum deformations of \(D=4\) Poincaré and Weyl algebra from \(q\)- deformed \(D=4\) conformal algebra (Q1909485)

The authors construct a \(q\)-deformation of the relativistic algebras as subalgebras and contractions of the real forms of the \(q\)-deformed \(\text{SL} (4, \mathbb{C})\), \(q\)-deformation of \(\text{SL} (4, \mathbb{C})\), performed in the standard way from a Cartan-Chevalley basis using Serre relations. The Lorentz quantum algebra and quantum Weyl algebra are defined as subalgebras of a real form of \(\text{SL}_q (4, \mathbb{C})\). A second form of \(q\)-deformed Poincaré algebras is obtained by a contraction of another real form of \(\text{SL}_q (4, \mathbb{C})\).