Endomorphism Algebras of Support τ-Tilting Modules

Let [Formula: see text] be a finite dimensional [Formula: see text]-algebra and [Formula: see text] be a support [Formula: see text]-tilting right [Formula: see text]-module. In this note, we give lower and upper bounds for the global dimension of the endomorphism algebra [Formula: see text] under some mild conditions. Finally, we give some examples to illustrate that both the upper and lower bounds can be reached.