Hopf Structures on Ambiskew Polynomial Rings
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 3dimensional Heisenberg Lie algebra. In a torsionfree case we describe the finitedimensional simple modules, in particular their dimensions and prove a ClebschGordan decomposition theorem for the tensor product of two simple modules. We construct a Casimir type operator and prove that any finitedimensional weight module is semisimple.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2005
 arXiv:
 arXiv:math/0510375
 Bibcode:
 2005math.....10375H
 Keywords:

 Mathematics  Rings and Algebras;
 Primary 16S36;
 Secondary 16W30;
 17B37
 EPrint:
 23 pages