Skew differential operator algebras of twisted Hopf algebras. (Q597136)

The author introduces a notion of `twisted Hopf algebras with generators'. This gives a common framework for studying some well-known structures, e.g, Lusztig's algebra, a member in Green's class, a \(\chi\)-bialgebra and a twisted Hopf algebra. The author studies skew differential operator algebras over twisted Hopf algebras with generators. This generalizes some basic facts in Weyl algebra to this general set up. Applying this to the twisted Ringel-Hall algebra the author gets a natural realization of the non-positive part of quantized generalized Kac-Moody algebra, by identifying the canonical generators with some linear, skew differential operators. This induces some algebras which are quantum group like.