Combinatorics of quasi-hereditary structures
| Autor: | Flores, Manuel, Kimura, Yuta, Rognerud, Baptiste |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Journal of Combinatorial Theory, Series A. Volume 187, April 2022 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jcta.2021.105559 |
| Popis: | A quasi-hereditary algebra is an Artin algebra together with a partial order on its set of isomorphism classes of simple modules which satisfies certain conditions. In this article we investigate all the possible choices that yield to quasi-hereditary structures on a given algebra, in particular we introduce and study what we call the poset of quasi-hereditary structures. Our techniques involve certain quiver decompositions and idempotent reductions. For a path algebra of Dynkin type $\mathbb{A}$, we provide a full classification of its quasi-hereditary structures. For types $\mathbb{D}$ and $\mathbb{E}$, we give a counting method for the number of quasi-hereditary structures. In the case of a hereditary incidence algebra, we present a necessary and sufficient condition for its poset of quasi-hereditary structures to be a lattice. Comment: 34 pages, 2 figures; typos corrected |
| Databáze: | arXiv |
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