Homological Bounds of Gentle algebras
Yu-Zhe Liu, Xin Ma, Jiacheng Xu, Chao Zhang
TL;DR
This paper investigates the homological bounds of gentle algebras, establishing conditions for upper bounds on module dimensions and characterizing quasi-tilted gentle algebras.
Contribution
It introduces new bounds for projective and injective dimensions in gentle algebras and characterizes quasi-tilted gentle algebras.
Findings
Upper bounds for homological dimensions established
Conditions for bounds less than twice the global dimension identified
Characterization of quasi-tilted gentle algebras provided
Abstract
This paper studies the homological bounds of gentle algebras, i.e., the upper bounds for the sum of the projective and injective dimensions of indecomposable modules over gentle algebras. We provide conditions under which this sum is strictly less than twice the global dimension, and as an application, we give a characterization of quasi-tilted gentle algebras.
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