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2 - τ-tilting Theory – an Introduction

Published online by Cambridge University Press:  25 November 2023

Edited by
David Jordan ,
Nadia Mazza  and
Sibylle Schroll
David Jordan
Affiliation:
University of Edinburgh
Nadia Mazza
Affiliation:
Lancaster University
Sibylle Schroll
Affiliation:
Universität zu Köln
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Summary

The notion of τ-tilting theory was introduced by Adachi, Iyama and Reiten at the beginning of the last decade and quickly became one of the most active areas of research in the representation theory of finite-dimensional algebras. The aim of these notes is two-fold. On the one hand, we want to give a friendly introduction to τ-tilting theory to anyone with a small background in representation theory. On the other, we want to fill the apparent gap for a survey on the subject by collecting in one place many of the most important results in τ-tilting theory.

Keywords

representations of finite-dimensional algebrasτ-tilting theorytorsion pairsstability conditionswall-and-chamber structures
Type
Chapter
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Modern Trends in Algebra and Representation Theory , pp. 46 - 108
Publisher: Cambridge University Press
Print publication year: 2023

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