Homological dimensions over almost gentle algebras

Abstract

We provide a method for computing the global dimension and self-injective dimension of almost gentle algebras,and prove that an almost gentle algebra is Gorenstein if it satisfies the Auslander condition.

Figures (19)

• Figure 2.1: An almost gentle pair
• Figure 2.2: String modules
• Figure 2.3: A band module
• Figure 2.4: An indecomposable module which is neither string nor band ($\lambda \ne 0$)
• Figure 3.1: The claw $s_1{\ \shortmid\mkern-13mu\wedge\ } s_2{\ \shortmid\mkern-13mu\wedge\ }\cdots{\ \shortmid\mkern-13mu\wedge\ } s_n$ given by directed strings $s_1, s_2, \ldots, s_n$

Theorems & Definitions (72)

• Theorem 1.2
• Theorem 1.3
• Theorem 1.4
• Definition 2.1
• Example 2.2
• Definition 2.3: String modules
• Remark 2.4
• Example 2.5
• Definition 3.1
• Lemma 3.2