Tilting complexes for group graded self-injective algebras

TL;DR

This paper develops a method to create derived equivalences between group graded self-injective algebras by extending known equivalences of their 1-components, enhancing understanding of their structural relationships.

Contribution

It introduces a new approach to derive equivalences for group graded self-injective algebras based on their 1-component equivalences, building on Rickard and Al-Nofayee's construction.

Findings

Derived equivalences constructed for group graded self-injective algebras.

Extension of 1-component equivalences to entire graded algebras.

Provides a framework for analyzing algebraic structures via grading.

Abstract

We construct derived equivalences between group graded self-injective algebras, starting from equivalences between their 1-components, obtained via a construction of J. Rickard and S. Al-Nofayee.