Abstract
We investigate some Hopf algebra structures over an Ore extension of a Hopf algebra. Necessary and sufficient conditions for an Ore extension of a Hopf algebra to have a Hopf algebra structure of a certain type are given. This construction, called a generalized Hopf–Ore extension, generalizes Hopf–Ore extensions. We describe the generalized Hopf–Ore extensions of the enveloping algebras of Lie algebras. For some Lie algebras g, the generalized Hopf–Ore extensions of U(g) are classified.
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