Singular equivalence of finite dimensional algebras with radical square zero

Abstract

We prove that the Crisp and Gow's quiver operation on a finite quiver Q produces a new quiver Q' with fewer vertices, such that the finite dimensional algebras kQ/J^2 and kQ'/J^2 are singularly equivalent. This operation is a general quiver operation which includes as specific examples some operations which arise naturally in symbolic dynamics (e.g., (elementary) strong shift equivalent, (in-out) splitting, source elimination, etc.).