Browsing by Subject "Derived Categories"

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    The Representation Theory of Transporter Categories
    (2022-05) Coopergard, Ryan
    In this paper, we extend the work of Diveris, Purin and Webb [5] to explore the structureof Auslander-Reiten quiver of Db(kP ⋊ G) and kP ⋊ G where G is a finite group, P is a finite poset, and P ⋊ G is the resulting transporter category. In particular, we show that given a transporter category P ⋊ G, a portion of the Auslander-Reiten quiver of Db(k[a, b] ⋊ Gb), where [a, b] ⋊ Gb is a subcategory which meets certain conditions. is copied into the Auslander-Reiten quiver of Db(kP ⋊ G). Moreover, we define a class of transporter categories, ICT, for which we can construct a slice of a component of the Auslander-Reiten quiver of Db(kP ⋊ G). This allows us to classify the transporter categories in ICT of finite representation type. We conclude with a connection to Young’s lattice of partitions.