Let H be a connected Hopf k-algebra of finite Gel'fand-Kirillov dimension
over an algebraically closed field k of characteristic 0. The objects of study
in this paper are the left or right coideal subalgebras T of H. They are shown
to be deformations of commutative polynomial k-algebras. A number of well-known
homological and other properties follow immediately from this fact. Further
properties are described, examples are considered, invariants are constructed
and a number of open questions are listed.Comment: 26 pages; comments welcom
