Indecomposables of the derived categories of certain associative algebras

TL;DR

This paper characterizes the indecomposable objects in the derived categories of a specific class of associative algebras, including gentle, skew-gentle, and some tubular algebra degenerations.

Contribution

It provides a description of indecomposables for a broad class of algebras, extending known results to new algebra types.

Findings

Classification of indecomposables for gentle and skew-gentle algebras

Extension of derived category analysis to certain tubular algebra degenerations

Enhanced understanding of the structure of derived categories for these algebras

Abstract

In this article we describe indecomposable objects of the derived categories of a branch class of associative algebras. To this class belong such known classes of algebras as gentle algebras, skew-gentle algebras and certain degenerations of tubular algebras.