Jordan-H\"older theorems for derived categories of derived discrete algebras

TL;DR

This paper classifies n-derived-simple derived discrete algebras up to derived equivalence and establishes Jordan-H"older theorems for their derived categories, advancing understanding of their structural properties.

Contribution

It provides a classification of n-derived-simple derived discrete algebras and proves Jordan-H"older theorems for their derived categories, a novel extension in the field.

Findings

Classification of n-derived-simple derived discrete algebras up to derived equivalence

Establishment of Jordan-H"older theorems for derived categories of these algebras

Enhanced understanding of the structure of derived discrete algebras

Abstract

For any positive integer $n$, $n$-derived-simple derived discrete algebras are classified up to derived equivalence. Furthermore, the Jordan-H\"older theorems for all kinds of derived categories of derived discrete algebras are obtained.