Lie Stack Deformations Original Research Article

Enveloping algebras of Lie stacks give irreducible Hopf algebra deformations ofU(image) 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(image) (usually with antipode of infinite order) whenever image has a codimension one Lie ideal image such that the quotient has the image-weight of an eigenvector of logical or operator2image.