On mutation of τ-tilting modules

ABSTRACT

Mutation of τ-tilting modules is a basic operation to construct a new support τ-tilting module from a given one by replacing a direct summand. The aim of this paper is to give a positive answer to the question posed in [2, Question 2.31] about mutation of τ-tilting modules.

KEYWORDS:

• τ-tilting modules
• mutation
• silting complexes

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16G10

Acknowledgment

This paper was written while the author was visiting Nagoya University from October 2015 to September 2016. The author thanks Prof. Osamu Iyama for the careful guidance and Prof. Zhaoyong Huang for the continuous encouragement. She thanks Yuya Mizuno for his valuable comments. She also wants to thank people in Nagoya University for their help. This work was partially supported by NSFC (Grant No. 11571164) and the China Scholarship Council (CSC).