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On Auslander-Reiten components of string complexes for a certain class of symmetric special biserial algebras by Giraldo, Hernán A.; Rueda-Robayo, Ricardo; Vélez-Marulanda, José A. is a scholarly article available to read on EtoBox.

What is On Auslander-Reiten components of string complexes for a certain class of symmetric special biserial algebras about?

Let $\mathbf{k}$ be an algebraically closed field. In this article, inspired by the description of indecomposable objects in the derived category of a gentle algebra obtained by V. Bekkert and H. A. Merklen, we define string complexes for a certain class $\mathscr{C}$ of symmetric special biserial algebras, which are indecomposable perfect complexes in the corresponding derived category. We also prove that if $\Lambda$ is a $\mathbf{k}$-algebra in the class $\mathscr{C}$ and $P^\bullet$ is a string complex over $\Lambda$, then $P^\bullet$ lies in the rim of its Auslander-Reiten component.

Author

Giraldo, Hernán A.; Rueda-Robayo, Ricardo; Vélez-Marulanda, José A.

Published

2020

Language

EN