  We give a Clifford correspondence for an algebra A over an algebraically
closed field, that is an algorithm for constructing some finite-dimensional
simple A-modules from simple modules for a subalgebra and endomorphism
algebras. This applies to all finite-dimensional simple A-modules in the case
that A is finite-dimensional and semisimple with a given semisimple subalgebra.
We discuss connections between our work and earlier results, with a view
towards applications particularly to finite-dimensional semisimple Hopf
algebras.
