A note on the $m$-extended module categories of Nakayama algebras
Endre S{\o}rmo Rundsveen

TL;DR
This paper investigates the structure of extended module categories of Nakayama algebras, providing classifications, algorithms, and explicit AR-quivers, thereby advancing understanding of their representation theory.
Contribution
It introduces new results on the existence of postprojective components and classifies finite type cases for extended module categories of Nakayama algebras.
Findings
Existence of postprojective components in certain extended module categories
Classification of Nakayama algebras of finite type in this context
Explicit AR-quivers for specific Nakayama algebras
Abstract
We study the extended module category of an algebra , recently introduced by Gupta and Zhou. The existence of a postprojective component of is shown for certain algebras , and a knitting algorithm through cohomological dimension vectors is provided. In particular, the extended module category of Nakayama algebras with homogeneous relations are investigated, and it is classified when they are of finite type. The paper give fully calculated AR-quivers for several Nakayama algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research
