Hopf Structures on Ambiskew Polynomial Rings
Artikel i vetenskaplig tidskrift, 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

Författare

Jonas Hartwig

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Journal of Algebra

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

Vol. 212 863-883

Ämneskategorier

Matematik

DOI

10.1016/j.jpaa.2007.07.010