Can I read $\tau$-Tilting modules over one-point extensions by a simple module at a source point on EtoBox?

$\tau$-Tilting modules over one-point extensions by a simple module at a source point by Gao, Hanpeng is a scholarly article available to read on EtoBox.

What is $\tau$-Tilting modules over one-point extensions by a simple module at a source point about?

Let $B$ be an one-point extension of a finite dimensional $k$-algebra $A$ by a simple $A$-module at a source point $i$. In this paper, we classify the $\tau$-tilting modules over $B$. Moreover, it is shown that there are equations $$|\tilt B|=|\tilt A|+|\tilt A/\langle e_i\rangle|\quad \text{and}\quad |\stilt B|=2|\stilt A|+|\stilt A/\langle e_i\rangle|.$$ As a consequence, we can calculate the numbers of $\tau$-tilting modules and support $\tau$-tilting modules over linearly Dynkin type algebras whose square radical are zero.

Author

Gao, Hanpeng

Published

2021

Language

EN