Hopf Structures on Ambiskew Polynomial Rings

Details Hopf Structures on Ambiskew Polynomial Rings Hopf Structures on Ambiskew Polynomial Rings

2005-10-18

arxiv.org/abs/math/0510375v1

Journal of Pure and Applied Algebra, 212 Issue 4 (2008), 863-883.

Mathematics

Rings and Algebras

23 pages

Scientific paper

10.1016/j.jpaa.2007.07.010

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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