关键词: Sweedler上同调, 正则上同调, 扭余作用, cleft余扩张

Abstract:

In this paper, we show that the twisted coactions of commutative Hopf algebras H on coalgebras C are invertible if the corresponding coassociators are convolution invertible. In this case, we define the regular cohomology and show that every invertible twisted coaction gives rise to a regular cohomology class of H with coefficients in C of degree three. We also show that the obstruction for $\rho$ vanishes if and only if the the twisted coaction ρ is corresponding to a cleft coextension.

Key words: Sweedler cohomology, Regular cohomology, Twisted coaction, Cleft coextension