The representation invariants of 2-term silting complexes

Let A be a finite dimensional k-algebra and P a 2-term silting complex in K-b (projA): In this article, we investigate the representation dimension of End(Db(A))(P) by the silting theory. We show that if P is a separating silting complex with certain homological restriction, then, rep.dim A = rep.dim End(Db(A))(P): This result generalizes the earlier result about tilting modules to the silting version. It is well-known that H-0 (P) is a support s-tilting module. We show that rep.dim End(A)(H-0 (P)) = rep.dim A=ann(A) (H-0(P)) whenever P is both separating and splitting. We apply this to obtain the corresponding consequence for support tau-tilting modules.