Endomorphism algebras of 2-term silting complexes

Abstract

We study possible values of the global dimension of endomorphism algebras of 2-term silting complexes. We show that for any algebra $A$ whose global dimension $gl.dimA\le 2$ and any 2-term silting complex $\mathbf{P}$ in the bounded derived category $D^b(A)$ of $A$, the global dimension of ${\mathrm{End}}_{D^b(A)}(\mathbf{P})$ is at most 7. We also show that for each $n>2$, there is an algebra $A$ with $gl.dimA=n$ such that $D^b(A)$ admits a 2-term silting complex $\mathbf{P}$ with $gl.dim{\mathrm{End}}_{D^b(A)}(\mathbf{P})$ infinite.

12 pages