运用上环理论解释弱Hopf代数

Weak Hopf Algebras Explained by Corings

弱双代数和弱Hopf代数是通常的双代数和Hopf代数的推广:定义的公理不变,但是余单位的乘法和单位的余乘法变得更弱一些了。将上环理论及其Galois理论运用于弱Hopf代数,得到弱Hopf代数的相应结果。对其对偶的情形进行了一定的研究,弱Hopf代数是有限广群代数的对偶。

Weak bialgebras and Hopf algebras are generalizations of ordinary bialgebras and Hopf algebras in the following sense： The defining axioms are the same, but the multiplicativity of the counit and comuhiplicativity of the unit are replaced by weaker axioms. The aim of this note is to develop the theory of corings and Galois theory for Hopf algebras. The dual situation where the weak Hopf algebra is the dual of a finite groupoid algebra is discussed.