Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra

Abstract

0.1. An important role in the theory of modular representations is played by certain finite dimensional Hopf algebras u over Fp (the field with p elements, p = prime). Originally, u was defined (Curtis [3]) as the restricted enveloping algebra of a simple Lie algebra over Fp For our purposes, it will be more convenient to define u as follows. Let us fix an indecomposable positive definite symmetric Cartan matrix