Abstract
An abelian Krull-Schmidt category is said to be uniserial if the isomorphism classes of subobjects of a given indecomposable object form a linearly ordered poset. In this paper, we classify the hereditary uniserial categories with Serre duality. They fall into two types: the first type is given by the representations of the quiver A n with linear orientation (and infinite variants thereof), the second type by tubes (and an infinite variant). These last categories give a new class of hereditary categories with Serre duality, called big tubes.
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van Roosmalen, AC. Hereditary Uniserial Categories with Serre Duality. Algebr Represent Theor 15, 1291–1322 (2012). https://doi.org/10.1007/s10468-011-9289-z
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DOI: https://doi.org/10.1007/s10468-011-9289-z