## Tsukuba Journal of Mathematics

### The Hopf algebra structure of a crossed product in a braided monoidal category

#### Abstract

In this paper we define conditions under which a tensor product $A \otimes H$, in a braided monoidal category, together with a crossed product structure $A \mathbin{\sharp_{\sigma}} H$ and a smash coproduct structure $A \propto H$ is a Hopf algebra. When $\sigma = \varepsilon_{H} \otimes \varepsilon_{H} \otimes \eta_{A}$, Radford's theorems characterizing the biproduct are obtained and when the antipode of $H$ is a $\sigma$-antipode we find an analogous result with the one due to Wang, Jiao and Zhao.

#### Article information

Source
Tsukuba J. Math., Volume 26, Number 2 (2002), 299-311.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164427

Digital Object Identifier
doi:10.21099/tkbjm/1496164427

Mathematical Reviews number (MathSciNet)
MR1940397

Zentralblatt MATH identifier
1025.18004

#### Citation

Alvarez, J. N. Alonso; Vilaboa, J. M. Fernández; Rodriguez, R. González. The Hopf algebra structure of a crossed product in a braided monoidal category. Tsukuba J. Math. 26 (2002), no. 2, 299--311. doi:10.21099/tkbjm/1496164427. https://projecteuclid.org/euclid.tkbjm/1496164427