ABSTRACT
P roof: The comultiplication formula (1) shows by a standard induc tive argument that
where by A we denote the usual wedge for subspaces of coalgebras. In particular An~1(kM ) = H, which implies by [3, Exercise 3.1.12] that Ho C kM . Since obviously kM C Ho, we obtain that Hq = kM , and the rest follows immediately from here. I
R em ark 1.2 Let C be the coalgebra defined in [7]. C has a basis { gi,d{ | i G Z ,i > 0 } and has the comultiplication and counit defined by
for any i > 0. We see that C is isomorphic as a coalgebra to H( 1,2, —l ) cop.
