Continuous Nakayama Representations

2022/07/08 by Rock, Job D., Zhu, Shijie · 2 citations
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2207.03908

Abstract

We introduce continuous analogues of Nakayama algebras. In particular, we introduce the notion of (pre-)Kupisch functions, which play a role as Kupisch series of Nakayama algebras, and view continuous Nakayama representations as a special type of representation of ℝ or \mathbbS¹. We investigate equivalences and connectedness of the categories of Nakayama representations. Specifically, we prove that orientation-preserving homeomorphisms on ℝ and on \mathbbS¹ induce equivalences between these categories. Connectedness is characterized by a special type of points called separation points determined by (pre-)Kupisch functions. We also construct an exact embedding from the category of finite-dimensional representations for any finite-dimensional Nakayama algebra, to a category of continuous Nakayama representaitons.

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