Hopf Structures on Ambiskew Polynomial Rings
Journal article, 2008

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(sl_2), U_q(sl_2) and the enveloping algebra of the three-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.

weight module

Hopf algebra

skew polynomial ring


Jonas Hartwig

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Journal of Algebra

0021-8693 (ISSN) 1090-266X (eISSN)

Vol. 212 4 863-883

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