2024/10/18 by Charles Paquette, Paquette, Charles, Job Daisie Rock +3 · 1 citation
Chemistry · Mathematics · #16G20 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Molecular spectroscopy and chirality #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2410.14656
openalex publication_date 2024/10/18 · openalex created_date 2024/11/02 · openalex updated_date 2026/07/28
We study the representation category of thread quivers and their quotients. A thread quiver is a quiver in which some arrows have been replaced by totally ordered sets. Pointwise finite-dimensional (pwf) representations of such a thread quiver admit a Krull-Remak-Schmidt-Azumaya decomposition. We show that an indecomposable representation is induced from an indecomposable representation of a quiver obtained from the original quiver by replacing some of its arrows by a finite linear \mathbbAn quiver. We study injective and projective pwf indecomposable representations and we fully classify them when the quiver satisfies a mild condition. We give a characterization of the indecomposable pwf representations of certain categories whose representation theory has similar properties to finite type or tame type. We further construct new hereditary abelian categories, including a Serre subcategory of pwf representations that includes every indecomposable representation.