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arXiv · 2408.09837

$\varrho$-Poincar\'e: bicrossproduct structure, $\star$-products and quantum Lie algebra

Luca Scala
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Abstract

We discuss the bicrossproduct structure of the quantum group $\varrho$-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 $\varrho$-Poincar\'e and noncommutative $\star$-products defined on the $\varrho$-Minkowski spacetime, analysing some of their relevant features. Furthermore, we comment on the role of physical bases and introduce the $\varrho$-Poincar\'e quantum Lie algebra.

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Luca Scala. 2024-08-19. $\varrho$-Poincar\'e: bicrossproduct structure, $\star$-products and quantum Lie algebra. https://arxiv.org/abs/2408.09837

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