On BD-algebra and CM-Auslander algebra for a gentle algebra and their representation types

Let $A$ be a gentle algebra, and $B$ and $C$ be its BD-gentle algebra and CM-Auslander algebra, respectively. In this paper, we show that the representation-finiteness of $A$, $B$ and $C$ coincide and the representation-discreteness of $A$, $B$ and $C$ coincide.

Publication Details

Journal
ArXiv.org
Published
2025-04-30
Primary Topic
Advanced Operator Algebra Research
Type
article
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article

On BD-algebra and CM-Auslander algebra for a gentle algebra and their representation types

ArXiv.org
Advanced Operator Algebra Research
article

On BD-algebra and CM-Auslander algebra for a gentle algebra and their representation types

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Abstract

Let $A$ be a gentle algebra, and $B$ and $C$ be its BD-gentle algebra and CM-Auslander algebra, respectively. In this paper, we show that the representation-finiteness of $A$, $B$ and $C$ coincide and the representation-discreteness of $A$, $B$ and $C$ coincide.

ArXiv.org
Openalex Percentile: Top 46%
Advanced Operator Algebra Research
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On BD-algebra and CM-Auslander algebra for a gentle algebra and their representation types · ArXiv.org (2025) | TGRS Research Map | TGRS