Geodesic
The classification of Nichols algebras over groups with finite root system of rank two
Journal of the European Mathematical Society, Tome 19 (2017) no. 7, pp. 1977-2017.

Voir la notice de l'article provenant de la source EMS Press

We classify all groups G and all pairs (V,W) of absolutely simple Yetter–Drinfeld modules over G such that the support of V⊕W generates G, cW,V​cV,W​=id, and the Nichols algebra of the direct sum of V and W admits a finite root system. As a byproduct, we determine the dimensions of such Nichols algebras, and several new families of finite-dimensional Nichols algebras are obtained. Our main tool is the Weyl groupoid of pairs of absolutely simple Yetter–Drinfeld modules over groups.
DOI : 10.4171/jems/711
Classification : 16-XX, 20-XX
Keywords: Hopf algebra, Nichols algebra, Weyl groupoid 
@article{JEMS_2017_19_7_a2,
     author = {Istv\'an Heckenberger and Leandro Vendramin},
     title = {The classification of {Nichols} algebras over groups with finite root system of rank two},
     journal = {Journal of the European Mathematical Society},
     pages = {1977--2017},
     publisher = {mathdoc},
     volume = {19},
     number = {7},
     year = {2017},
     doi = {10.4171/jems/711},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/711/}
}
TY  - JOUR
AU  - István Heckenberger
AU  - Leandro Vendramin
TI  - The classification of Nichols algebras over groups with finite root system of rank two
JO  - Journal of the European Mathematical Society
PY  - 2017
SP  - 1977
EP  - 2017
VL  - 19
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/711/
DO  - 10.4171/jems/711
ID  - JEMS_2017_19_7_a2
ER  - 
%0 Journal Article
%A István Heckenberger
%A Leandro Vendramin
%T The classification of Nichols algebras over groups with finite root system of rank two
%J Journal of the European Mathematical Society
%D 2017
%P 1977-2017
%V 19
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/711/
%R 10.4171/jems/711
%F JEMS_2017_19_7_a2
István Heckenberger; Leandro Vendramin. The classification of Nichols algebras over groups with finite root system of rank two. Journal of the European Mathematical Society, Tome 19 (2017) no. 7, pp. 1977-2017. doi : 10.4171/jems/711. http://geodesic.mathdoc.fr/articles/10.4171/jems/711/

Cité par Sources :