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Derived equivalences and delooping levels

Liang Chen

Abstract

We construct a finite-dimensional algebra derived equivalent to the example of Kershaw--Rickard. For the Kershaw--Rickard example the delooping level and the sub-derived delooping level are both infinite, while for our algebra both invariants are $0$. Thus the finiteness of these invariants is not preserved under derived equivalences.

Derived equivalences and delooping levels

Abstract

We construct a finite-dimensional algebra derived equivalent to the example of Kershaw--Rickard. For the Kershaw--Rickard example the delooping level and the sub-derived delooping level are both infinite, while for our algebra both invariants are . Thus the finiteness of these invariants is not preserved under derived equivalences.
Paper Structure (2 sections, 9 theorems, 16 equations)

This paper contains 2 sections, 9 theorems, 16 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['thm:main']}

Key Result

Theorem 1.1

There exist derived equivalent finite-dimensional algebras $B$ and $C$ over a field $k$ such that

Theorems & Definitions (19)

  • Theorem 1.1
  • Definition 2.1: Gelinas22Adv
  • Definition 2.2: GuoIgusa25
  • Remark 2.3
  • Lemma 2.4: KR24, GuoIgusa25
  • Lemma 2.5
  • proof
  • Lemma 2.6: Ladkani Ladkani11
  • Corollary 2.7
  • proof
  • ...and 9 more