Support τ-tilting modules over one-point extensions

Abstract

Let B be the one-point extension algebra of A by an A-module X. We proved that every support τ-tilting A-module can be extended to be a support τ-tilting B-module by two different ways. As a consequence, it is shown that there is an inequality $$|\mathrm{s}\tau ‐\text{tilt\hspace{0.17em}}\mathrm{\hspace{0.17em}}B|⩾2|\mathrm{s}\tau ‐\text{tilt\hspace{0.17em}}A|.$$

Keywords:

• One-point extensions
• semibricks
• support τ-tilting modules

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16E30
• 16G20

Acknowledgment

The authors would like to thank Professor Zhaoyong Huang and Dong Yang for continuous encouragement.

Additional information

Funding

This work was partially supported by National Natural Science Foundation of China (Grant No. 11971225).