Geodesic
The Complexity of Crossed Products
Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 407-412.

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Let $H$ be a finite-dimensional Hopf algebra, $A$ be a finite-dimensional algebra measured by $H$ and $A\mathbin{\#_\sigma}H$ be a crossed product. In this paper, we first show that if $H$ is semisimple as well as its dual $H^*$, then the complexity of $A\mathbin{\#_\sigma} H$ is equal to that of $A$. Furthermore, we prove that the complexity of a finite-dimensional Hopf algebra $H$ is equal to the complexity of the trivial module $_Hk$. As an application, we prove that the complexity of Sweedler's 4-dimensional Hopf algebra $H_4$ is equal to $1$.
Keywords: crossed product, complexity, trivial module, Sweedler's 4-dimensional Hopf algebra. 
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     title = {The {Complexity} of {Crossed} {Products}},
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Ling Liu; Bing-Liang Shen. The Complexity of Crossed Products. Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 407-412. http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a8/

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