Hicas of length 4\le 4.

  • Vanessa Miemietz

    School of Mathematics Department of Mathematics University of East Anglia University of Aberdeen Norwich, NR4 7TJ, UK Fraser Noble Building
  • Will Turner

    King's College Aberdeen AB24 3UE, UK
Hicas of length $\le 4$. cover
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A hica is a highest weight, homogeneous, indecomposable, Calabi-Yau category of dimension 0. A hica has length ll if its objects have Loewy length ll and smaller. We classify hicas of length <=4<= 4, up to equivalence, and study their properties. Over a fixed field FF, we prove that hicas of length 4 are in one-one correspondence with bipartite graphs. We prove that an algebra AΓA_\Gamma controlling the hica associated to a bipartite graph Γ\Gamma is Koszul, if and only if Γ\Gamma is not a simply laced Dynkin graph, if and only if the quadratic dual of AΓA_\Gamma is Calabi-Yau of dimension 3.

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Vanessa Miemietz, Will Turner, Hicas of length 4\le 4.. Doc. Math. 15 (2010), pp. 177–205

DOI 10.4171/DM/294