Geodesic
Geometric combinatorics of Weyl groupoids
Journal of Algebraic Combinatorics, Tome 34 (2011) no. 1, pp. 115-139.

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

Summary: We extend properties of the weak order on finite Coxeter groups to Weyl groupoids admitting a finite root system. In particular, we determine the topological structure of intervals with respect to weak order, and show that the set of morphisms with fixed target object forms an ortho-complemented meet semilattice. We define the Coxeter complex of a Weyl groupoid with finite root system and show that it coincides with the triangulation of a sphere cut out by a simplicial hyperplane arrangement. As a consequence, one obtains an algebraic interpretation of many hyperplane arrangements that are not reflection arrangements.
Mots-clés : keywords Coxeter complex, simplicial arrangements, weak order, Weyl groupoid 
@article{JAC_2011__34_1_a1,
     author = {Heckenberger, Istv\'an and Welker, Volkmar},
     title = {Geometric combinatorics of {Weyl} groupoids},
     journal = {Journal of Algebraic Combinatorics},
     pages = {115--139},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2011},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/JAC_2011__34_1_a1/}
}
TY  - JOUR
AU  - Heckenberger, István
AU  - Welker, Volkmar
TI  - Geometric combinatorics of Weyl groupoids
JO  - Journal of Algebraic Combinatorics
PY  - 2011
SP  - 115
EP  - 139
VL  - 34
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/JAC_2011__34_1_a1/
LA  - en
ID  - JAC_2011__34_1_a1
ER  - 
%0 Journal Article
%A Heckenberger, István
%A Welker, Volkmar
%T Geometric combinatorics of Weyl groupoids
%J Journal of Algebraic Combinatorics
%D 2011
%P 115-139
%V 34
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/JAC_2011__34_1_a1/
%G en
%F JAC_2011__34_1_a1
Heckenberger, István; Welker, Volkmar. Geometric combinatorics of Weyl groupoids. Journal of Algebraic Combinatorics, Tome 34 (2011) no. 1, pp. 115-139. https://geodesic-test.mathdoc.fr/item/JAC_2011__34_1_a1/