A new characterization of quasi-hereditary Nakayama algebras and applications

Marczinzik, René; Sen, Emre

doi:10.1080/00927872.2022.2063301

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“…In [17], Sen characterizes Nakayama algebras which are higher Auslander. In [12], the authors classifies quasi-hereditary Nakayama algebras.…”

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confidence: 99%

Continuous Nakayama Representations

Rock¹,

Zhu²

2022

Preprint

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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 S 1 . We investigate equivalences and connectedness of the categories of Nakayama representations. Specifically, we prove that orientation-preserving homeomorphisms on R and on S 1 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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“…In [17], Sen characterizes Nakayama algebras which are higher Auslander. In [12], the authors classifies quasi-hereditary Nakayama algebras.…”

mentioning

confidence: 99%