Braided symmetries of $SU_{q,\phi}(2)$ and Podle\'s Spheres

Andrzej Sitarz; Rafa{\l} Bistro\'n

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Braided symmetries of $SU_{q,\phi}(2)$ and Podle\'s Spheres

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arxiv 2109.14605 v2 pith:VONBSRNF submitted 2021-09-29 math.QA math.RA

Rafa{l} Bistroń , Andrzej Sitarz This is my paper · ORCID

classification math.QAmath.RA

keywords braidedhopfalgebraquantumspheressymmetriesalgebrascompatibility

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abstract

We present an explicit form of braided symmetries of the quantum spheres, by introducing a braided quantum Hopf algebra $\cU_{q, \phi}$ and demonstrating that they are braided Hopf modules over this braided Hopf algebra. To obtain this result, we systematically develop braided versions of structures like pairing between Hopf algebras, left module algebra as well as their compatibility with the $*$-structure.

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