Hicas of length .
Vanessa MiemietzSchool of Mathematics Department of Mathematics University of East Anglia University of Aberdeen Norwich, NR4 7TJ, UK Fraser Noble Building
Will TurnerKing's College Aberdeen AB24 3UE, UK
A hica is a highest weight, homogeneous, indecomposable, Calabi-Yau category of dimension 0. A hica has length if its objects have Loewy length and smaller. We classify hicas of length , up to equivalence, and study their properties. Over a fixed field , we prove that hicas of length 4 are in one-one correspondence with bipartite graphs. We prove that an algebra controlling the hica associated to a bipartite graph is Koszul, if and only if is not a simply laced Dynkin graph, if and only if the quadratic dual of is Calabi-Yau of dimension 3.
Cite this article
Vanessa Miemietz, Will Turner, Hicas of length .. Doc. Math. 15 (2010), pp. 177–205DOI 10.4171/DM/294