THE REGULAR COMPONENTS OF THE AUSLANDER-REITEN QUIVER OF ATILTED ALGEBRA
Citation：
Claus Michael ringel.THE REGULAR COMPONENTS OF THE AUSLANDER-REITEN QUIVER OF ATILTED ALGEBRA[J].Chinese Annals of Mathematics B,1988,9(1):1~18
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Authors：
Claus Michael ringel;
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 $\[\Gamma (A)\]$ of a tilted algebra $A$. The second result asserts that for a tilted algebra $A$,any regular component of $\[\Gamma (A)\]$ which is not a connecting component, is quasi-serial.
