Tameness and Local Normal Bases for Objects of Finite Hopf Algebras

Lindsay N. Childs, Susan Hurley
1986 Transactions of the American Mathematical Society  
Let R be a commutative ring, S an fí-algebra, H a Hopf Ralgebra, both finitely generated and projective as /¿-modules, and suppose S is an //-object, so that H* = Hotcir(H, R) acts on S via a measuring. Let / be the space of left integrals of //*. We say S has normal basis if S = H as H*modules, and S has local normal bases if Sp = Hv as //'-modules for all prime ideals p of R. When R is a perfect field, H is commutative and cocommutative, and certain obvious necessary conditions on S hold,
more » ... ions on S hold, then S has normal basis if and only if IS = R = SH . If R is a domain with quotient field K, H is cocommutative, and L = S ®ñ K has normal basis as (//* ® /f)-module, then S has local normal bases if and only if IS = R = SH .
doi:10.2307/2000648 fatcat:6rahounyubdubp6johmgxb7kpq