交换Hopf代数扭余作用下的余代数的上同调

Abstract

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

CLC Number:

16W30

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JU Teng-Xia. Cohomology for Coalgebras with Twisted Coactions of Commutative Hopf Algebras[J].Acta mathematica scientia,Series A, 2010, 30(1): 179-196.

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References

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Cohomology for Coalgebras with Twisted Coactions of Commutative Hopf Algebras

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