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Hopf Structures on Ambiskew Polynomial Rings

Jonas T. Hartwig
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Abstract

We derive necessary and sufficient conditions for an ambiskew polynomial ring to have a Hopf algebra structure of a certain type. This construction generalizes many known Hopf algebras, for example U(sl2), U_q(sl2) and the enveloping algebra of the 3-dimensional Heisenberg Lie algebra. In a torsion-free case we describe the finite-dimensional simple modules, in particular their dimensions and prove a Clebsch-Gordan decomposition theorem for the tensor product of two simple modules. We construct a Casimir type operator and prove that any finite-dimensional weight module is semisimple.

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BibTeXRIS

Jonas T. Hartwig. 2005-10-18. Hopf Structures on Ambiskew Polynomial Rings. https://doi.org/10.1016/j.jpaa.2007.07.010

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