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

Voir la notice de l'article provenant de la source 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/}
}
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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/