## Taiwanese Journal of Mathematics

### MASCHKE-TYPE THEOREM AND DUALITY THEOREM FOR WEAK TWISTED SMASH PRODUCTS

Xiao-yan Zhou

#### Abstract

Let $H$ be a weak Hopf algebra in the sense of Böhm and Szlachányi [3] and $A$ a weak $H$-bimodule algebra. Then in this paper we first introduce the notion of a weak twisted smash product $A \star H$ and then find some sufficient and necessary conditions making it into a weak bialgebra. Furthermore, we give a Maschke-type theorem for the weak twisted smash product over semisimple weak Hopf algebra $H$, which generalizes the well-known Maschke-type theorem in [5, 15, 17]. Finally, we obtain an analogue of the duality theorem for the weak twisted smash products.

#### Article information

Source
Taiwanese J. Math., Volume 15, Number 6 (2011), 2701-2719.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406492

Digital Object Identifier
doi:10.11650/twjm/1500406492

Mathematical Reviews number (MathSciNet)
MR2896139

Zentralblatt MATH identifier
1257.16029

Subjects
Primary: 16W30

#### Citation

Zhou, Xiao-yan. MASCHKE-TYPE THEOREM AND DUALITY THEOREM FOR WEAK TWISTED SMASH PRODUCTS. Taiwanese J. Math. 15 (2011), no. 6, 2701--2719. doi:10.11650/twjm/1500406492. https://projecteuclid.org/euclid.twjm/1500406492

#### References

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