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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2013_93_3_a8,
     author = {Ling Liu and Bing-Liang Shen},
     title = {The {Complexity} of {Crossed} {Products}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {407--412},
     publisher = {mathdoc},
     volume = {93},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a8/}
}
TY  - JOUR
AU  - Ling Liu
AU  - Bing-Liang Shen
TI  - The Complexity of Crossed Products
JO  - Matematičeskie zametki
PY  - 2013
SP  - 407
EP  - 412
VL  - 93
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a8/
LA  - ru
ID  - MZM_2013_93_3_a8
ER  - 
%0 Journal Article
%A Ling Liu
%A Bing-Liang Shen
%T The Complexity of Crossed Products
%J Matematičeskie zametki
%D 2013
%P 407-412
%V 93
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a8/
%G ru
%F MZM_2013_93_3_a8
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/