S. Caenepeel et al., COALGEBRA DEFORMATIONS OF BIALGEBRAS BY HARRISON COCYCLES, COPAIRINGSOF HOPF ALGEBRAS AND DOUBLE CROSSCOPRODUCTS, Bulletin of the Belgian Mathematical Society Simon Stevin, 4(5), 1997, pp. 647-671
We study how the comultiplication on a Hopf algebra can be modified in
such a way that the new comultiplication together with the original m
ultiplication and a suitable antipode gives a new Hopf algebra. To thi
s end, we have to study Harrison type cocycles, and it turns out that
there is a relation with the Yang-Baxter equation. The construction is
applied to deform the coalgebra structure on the tensor product of tw
o bialgebras using a copairing. This new bialgebra can be viewed as a
double crosscoproduct. It is also shown that a crossed coproduct over
an inner comeasuring is isomorphic to a twisted coproduct.