
arXiv: 2301.05956
We show that the order type of the simplest version of a hammock for string algebras lies in the class of finite description linear orders--the smallest class of linear orders containing $\mathbf 0$, $\mathbf 1$, and that is closed under isomorphisms, finite order sum, anti-lexicographic product with $ω$ and $ω^*$, and shuffle of finite subsets--using condensation (localization) of linear orders as a tool. We also introduce two finite subsets of the set of bands and use them to describe the location of left $\mathbb N$-strings in the completion of hammocks.
30 pages, 5 figures
hammock, Mathematics - Rings and Algebras, finite description linear order, 16G20, non-domestic, Rings and Algebras (math.RA), FOS: Mathematics, Representations of quivers and partially ordered sets, string algebra, Representation Theory (math.RT), Mathematics - Representation Theory
hammock, Mathematics - Rings and Algebras, finite description linear order, 16G20, non-domestic, Rings and Algebras (math.RA), FOS: Mathematics, Representations of quivers and partially ordered sets, string algebra, Representation Theory (math.RT), Mathematics - Representation Theory
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