Hicas of length $\le 4$.
Documenta mathematica, Tome 15 (2010), pp. 177-205.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: A hica is a highest weight, homogeneous, indecomposable, Calabi-Yau category of dimension 0. A hica has length $l$ if its objects have Loewy length $l$ and smaller. We classify hicas of length $= 4$, up to equivalence, and study their properties. Over a fixed field $F$, we prove that hicas of length 4 are in one-one correspondence with bipartite graphs. We prove that an algebra $A_\Gamma$ controlling the hica associated to a bipartite graph $\Gamma$ is Koszul, if and only if $\Gamma$ is not a simply laced Dynkin graph, if and only if the quadratic dual of $A_\Gamma$ is Calabi-Yau of dimension 3.
Classification : 05, 14, 16, 18 
@article{DOCMA_2010__15__a30,
     author = {Miemietz, Vanessa and Turner, Will},
     title = {Hicas of length $\le 4$.},
     journal = {Documenta mathematica},
     pages = {177--205},
     publisher = {mathdoc},
     volume = {15},
     year = {2010},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a30/}
}
TY  - JOUR
AU  - Miemietz, Vanessa
AU  - Turner, Will
TI  - Hicas of length $\le 4$.
JO  - Documenta mathematica
PY  - 2010
SP  - 177
EP  - 205
VL  - 15
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a30/
LA  - en
ID  - DOCMA_2010__15__a30
ER  - 
%0 Journal Article
%A Miemietz, Vanessa
%A Turner, Will
%T Hicas of length $\le 4$.
%J Documenta mathematica
%D 2010
%P 177-205
%V 15
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a30/
%G en
%F DOCMA_2010__15__a30
Miemietz, Vanessa; Turner, Will. Hicas of length $\le 4$.. Documenta mathematica, Tome 15 (2010), pp. 177-205. https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a30/