The Representation Theory of Transporter Categories
2022-05
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The Representation Theory of Transporter Categories
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2022-05
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Abstract
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.
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University of Minnesota Ph.D. dissertation. May 2022. Major: Mathematics. Advisor: Peter Webb. 1 computer file (PDF); iv, 95 pages.
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Coopergard, Ryan. (2022). The Representation Theory of Transporter Categories. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/241373.
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