Geodesic
Hicas of length $\le 4$.
Documenta mathematica, Tome 15 (2010), pp. 177-205
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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 AΓ​ controlling the hica associated to a bipartite graph Γ is Koszul, if and only if Γ is not a simply laced Dynkin graph, if and only if the quadratic dual of AΓ​ is Calabi–Yau of dimension 3.
DOI : 10.4171/dm/294
Classification : 05, 14, 16, 18 
@article{10_4171_dm_294,
     author = {Will Turner and Vanessa Miemietz},
     title = {Hicas of length $\le 4$.},
     journal = {Documenta mathematica},
     pages = {177--205},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/294},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/294/}
}
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Will Turner; Vanessa Miemietz. Hicas of length $\le 4$.. Documenta mathematica, Tome 15 (2010), pp. 177-205. doi: 10.4171/dm/294

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