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We discuss the bicrossproduct structure of the quantum group -Poincar\'e and of the dual quantum universal enveloping algebra, expanding the construction to general Lie algebra-type deformations of Poincar\'e coming from classical r-matrices. We review the relation between different bases of the quantum universal enveloping algebra of -Poincar\'e and noncommutative -products defined on the -Minkowski spacetime, analysing some of their relevant features. Furthermore, we comment on the role of physical bases and introduce the -Poincar\'e quantum Lie algebra.
Luca Scala (2024) studied this question.
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