A study of Blattner-Montgomery duality in weak Hopf algebras of groupoid algebras type

Duality for groupoid (co)actions

In this paper we present Cohen-Montgomery-type duality theorems for groupoid (co)actions.

交换环上霍普夫代数的对偶与有理模

Duality and Rational Modules in Hopf Algebras over Commutative Rings

设$A$是交换环$R$上的代数.若$R$是Noether模，而$A^\circ$在$R^A$中是纯模，则有理左$A$ -模范畴与有理右$A^\circ$ -余模范畴是同构的.在霍普夫代数的情况下，我们也可以加强Blattner-Montgomery对偶定理。最后给出了$R^A$中$A^\circ$纯度的充分条件。

环上交叉积的对偶定理

Duality Theorems for Crossed Products over Rings

本文推广了M. Koppinen和C. Chen从基域或戴德金整环的情形推广到任意Noether交换基环的情形。特别是，我们延长了改进版本的著名的布拉特纳-蒙哥马利对偶定理的情况下，任意诺特地环。

无穷辫子霍普夫代数的对偶定理

Duality Theorems for Infinite Braided Hopf Algebras

设$H$是一个无穷维辫状霍普夫代数，并假设辫状是关于$H$及其拟对偶$H^d$对称的.证明了Blattner-Montgomery对偶定理，即证明了$$ (R # H)# H^{d} \cong R \otimes (H # H^{d}) \hbox {as algebras in braided tensor category} {\cal C}.$$。特别地，我们给出了Yetter-Drinfeld模范畴中无限辫子霍普夫代数的两个对偶定理。

Enveloping actions and duality theorems for partial twisted smash products

In this paper, we first generalize the theorem about the existence of an enveloping action to a partial twisted smash product. Second, we construct a Morita context between the partial twisted smash product and the twisted smash product related to the enveloping action. Furthermore, we show some results relating partial actions and partial representations over the partial twisted smash products, which generalize the results of Alves and Batista (Comm. Algebra, 38(8): 2872-2902, 2010). Finally, we present versions of the duality theorems of Blattner-Montgomery for partial twisted smash products…

Globalization theorems for partial Hopf (co)actions, and some of their applications

Partial actions of Hopf algebras can be considered as a generalization of partial actions of groups on algebras. Among important properties of partial Hopf actions, it is possible to prove the existence of enveloping actions, i.e., every partial Hopf action on a algebra A is induced by a Hopf action on a algebra B that contains A as a right ideal. This globalization theorem allows to extend several results from the theory of partial group actions to the Hopf algebraic setting. In this article, we prove a dual version of the globalization theorem: that every partial coaction of a Hopf algebra a…