$\varrho$-Poincaré: bicrossproduct structure, $\star$-products and quantum Lie algebra
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914954223812608 |
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| author | Scala, Luca |
| author_facet | Scala, Luca |
| contents | We discuss the bicrossproduct structure of the quantum group $\varrho$-Poincaré and of the dual quantum universal enveloping algebra, expanding the construction to general Lie algebra-type deformations of Poincaré coming from classical $r$-matrices. We review the relation between different bases of the quantum universal enveloping algebra of $\varrho$-Poincaré 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 $\varrho$-Poincaré quantum Lie algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\varrho$-Poincaré: bicrossproduct structure, $\star$-products and quantum Lie algebra Scala, Luca High Energy Physics - Theory We discuss the bicrossproduct structure of the quantum group $\varrho$-Poincaré and of the dual quantum universal enveloping algebra, expanding the construction to general Lie algebra-type deformations of Poincaré coming from classical $r$-matrices. We review the relation between different bases of the quantum universal enveloping algebra of $\varrho$-Poincaré 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 $\varrho$-Poincaré quantum Lie algebra. |
| title | $\varrho$-Poincaré: bicrossproduct structure, $\star$-products and quantum Lie algebra |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2408.09837 |