τ-Tilting modules over one-point extensions by a simple module at a source point.

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 τ -tilting modules over B. Moreover, it is shown that there are equations | τ − tilt B | = | τ − tilt A | + | τ − tilt A / 〈 e i 〉 | and | s τ − tilt B | = 2 | s τ − tilt A | + | s τ − tilt A / 〈 e i 〉 |. As a consequence, we can calculate the numbers of τ -tilting modules and support τ -tilting modules over linearly Dynkin type algebras whose square radical are zero. [ABSTRACT FROM AUTHOR]