BICOVARIANT DIFFERENTIAL CALCULI FOR FINITE GLOBAL QUOTIENTS

Let (M, G) be a finite global quotient;, a finite set tl with an action by a finite group G. In this note, we classify all bicovariant first order differential calculi (FODCs) over the weak Hopf algebra k(C proportional to M) similar or equal to kV; proportional to M]*, where G proportional to M is the action groupoid associated to (NI, (7), and k[C proportional to M] is the groupoid algebra of G proportional to M. Specifically, we prove a necessary and sufficient condition for a FODC over k(G proportional to NI) to be bicovariant and then show that the isomorphism classes of bicovariant FODCs over ki(C a M) are in one-to-one correspondence with subsets of a certain quotient space.