THE REGULAR COMPONENTS OF THE AUSLANDER-REITEN QUIVER OF A TILTED ALGEBRA

Abstract

Let B be a connected finite-dimensional hereditary algebra of infinite representation type.It is shown that there exists a regular tilting B-module if and only if B is wild and has at least three simple modules.In this way,the author determines the possible form of regular components which arise as a connecting component of the Auslander-Reiten quiver Γ(A)of a tilted algebra A.The second result asserts that for a tilted algebra A, any regular component of Γ(A)which is not a connecting component,is quasi-serial.