Geodesic
Generalized cluster complexes via quiver representations.
Journal of Algebraic Combinatorics, Tome 27 (2008) no. 1, pp. 35-54.

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

Summary: We give a quiver representation theoretic interpretation of generalized cluster complexes defined by Fomin and Reading. Using $d$-cluster categories defined by Keller as triangulated orbit categories of (bounded) derived categories of representations of valued quivers, we define a $d$-compatibility degree ( - $\parallel $ - ) on any pair of "colored" almost positive real Schur roots which generalizes previous definitions on the noncolored case and call two such roots compatible, provided that their $d$-compatibility degree is zero. Associated to the root system $\Phi $ corresponding to the valued quiver, using this compatibility relation, we define a simplicial complex which has colored almost positive real Schur roots as vertices and $d$-compatible subsets as simplices. If the valued quiver is an alternating quiver of a Dynkin diagram, then this complex is the generalized cluster complex defined by Fomin and Reading.
Classification : 05A15, 16G20, 16G70, 17B20
Keywords: keywords colored almost positive real Schur root, generalized cluster complex, $d$-cluster category, $d$-cluster tilting object, $d$-compatibility degree 
@article{JAC_2008__27_1_a3,
     author = {Zhu, Bin},
     title = {Generalized cluster complexes via quiver representations.},
     journal = {Journal of Algebraic Combinatorics},
     pages = {35--54},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2008__27_1_a3/}
}
TY  - JOUR
AU  - Zhu, Bin
TI  - Generalized cluster complexes via quiver representations.
JO  - Journal of Algebraic Combinatorics
PY  - 2008
SP  - 35
EP  - 54
VL  - 27
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2008__27_1_a3/
LA  - en
ID  - JAC_2008__27_1_a3
ER  - 
%0 Journal Article
%A Zhu, Bin
%T Generalized cluster complexes via quiver representations.
%J Journal of Algebraic Combinatorics
%D 2008
%P 35-54
%V 27
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2008__27_1_a3/
%G en
%F JAC_2008__27_1_a3
Zhu, Bin. Generalized cluster complexes via quiver representations.. Journal of Algebraic Combinatorics, Tome 27 (2008) no. 1, pp. 35-54. http://geodesic.mathdoc.fr/item/JAC_2008__27_1_a3/