Hopf algebras of low dimension

The main aim of this paper is to classify all types of Hopf algebras of dim ension less thn or equal to 11 over an algebraically closed field of charac teristic 0. If A is such a Hopf algebra that is not semisimple, then we sha ll prove that A or A* is pointed. This property will result from the fact t hat, under some assumptions, any Hopf algebra that is generated as an algeb ra by a four-dimensional simple subcoalgebra is a Hopf quotient of the coor dinate ring of quantum SL2(k). The first result allows us to reduce the cla ssification to the case of pointed Hopf algebras of dimension 8. We shall d escribe their types in the last part of the paper. (C) 1999 Academic Press.