Geodesic
Graded cluster algebras
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 1111-1134.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra theory to the foreground and promote its study. We transfer a definition of Gekhtman, Shapiro and Vainshtein to the algebraic setting, yielding the notion of a multi-graded cluster algebra. We then study gradings for finite-type cluster algebras without coefficients, giving a full classification. Translating the definition suitably again, we obtain a notion of multi-grading for (generalised) cluster categories. This setting allows us to prove additional properties of graded cluster algebras in a wider range of cases. We also obtain interesting combinatorics -- namely tropical frieze patterns -- on the Auslander-Reiten quivers of the categories.
Classification : 13F60, 18E30, 16G70
Keywords: cluster algebra, graded, cluster category, tropical frieze 
@article{JAC_2015__42_4_a1,
     author = {Grabowski, Jan E.},
     title = {Graded cluster algebras},
     journal = {Journal of Algebraic Combinatorics},
     pages = {1111--1134},
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2015__42_4_a1/}
}
TY  - JOUR
AU  - Grabowski, Jan E.
TI  - Graded cluster algebras
JO  - Journal of Algebraic Combinatorics
PY  - 2015
SP  - 1111
EP  - 1134
VL  - 42
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2015__42_4_a1/
LA  - en
ID  - JAC_2015__42_4_a1
ER  - 
%0 Journal Article
%A Grabowski, Jan E.
%T Graded cluster algebras
%J Journal of Algebraic Combinatorics
%D 2015
%P 1111-1134
%V 42
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2015__42_4_a1/
%G en
%F JAC_2015__42_4_a1
Grabowski, Jan E. Graded cluster algebras. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 1111-1134. http://geodesic.mathdoc.fr/item/JAC_2015__42_4_a1/