The representation invariants of 2-term silting complexes

Abstract

Let A be a finite dimensional k-algebra and P a 2-term silting complex in In this article, we investigate the representation dimension of by the silting theory. We show that if P is a separating silting complex with certain homological restriction, then, rep.dim A = rep.dim This result generalizes the earlier result about tilting modules to the silting version. It is well-known that is a support τ-tilting module. We show that rep.dim rep.dim whenever P is both separating and splitting. We apply this to obtain the corresponding consequence for support τ-tilting modules.