Hopf Structures on Ambiskew Polynomial Rings

@article{Hartwig2008HopfSO,
  title={Hopf Structures on Ambiskew Polynomial Rings},
  author={J. Hartwig},
  journal={Journal of Pure and Applied Algebra},
  year={2008},
  volume={212},
  pages={863-883}
}
  • J. Hartwig
  • Published 2008
  • Mathematics
  • Journal of Pure and Applied Algebra
  • 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… CONTINUE READING
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