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Quantum deformations of $$D=4$$ Poincaré and Weyl algebra from $$q$$- deformed $$D=4$$ conformal algebra. (English) Zbl 0834.17021
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 $$\text{SL}_q (4, \mathbb{C})$$.

##### MSC:
 17B37 Quantum groups (quantized enveloping algebras) and related deformations 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 16S30 Universal enveloping algebras of Lie algebras
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