Authors
Yu-Zhe Liu, Panyue Zhou
Fields
Keypoints
The paper examines the representation theory of string almost gentle (SAG) algebras.
It shows that the representation types of an SAG algebra, its endomorphism algebra, and the Cohen-Macaulay Auslander algebra are equivalent.
The results extend previous findings on the representation-finiteness of gentle algebras.
Summary
The authors investigate the representation theory of string almost gentle (SAG) algebras, establishing new connections between these algebras and their endomorphism algebras. They define specific subsets R of the quiver's arrow set and introduce finitely generated modules M_R and their corresponding endomorphism algebras A_R. A key result is that the representation type of an SAG-algebra A, the R-endomorphism algebra A_R, and the Cohen-Macaulay Auslander algebra A_CMA are equivalent. The paper demonstrates that the representation types of these algebras are structurally linked, extending previous findings on the representation-finiteness of gentle algebras, and providing new insights into endomorphism algebras. Furthermore, the authors show that for certain subsets R, the endomorphism algebras A_R exhibit a representation type similar to that of the Cohen-Macaulay Auslander algebra, offering a thorough classification of the algebraic properties of SAG-algebras.
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