Abstract
Enveloping algebras of Lie stacks give irreducible Hopf algebra deformations ofU(g) which are neither commutative nor cocommutative. In this paper we present and study a large class of examples of Lie stacks. In particular, we show that the PBW-bases of these Hopf algebras do not have to be finite in general. Further, we construct a non-cocommutative Hopf structure onU(g) (usually with antipode of infinite order) whenever g has a codimension one Lie ideal h such that the quotient has the h-weight of an eigenvector of ⋀2h.
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