On the number of tilting modules over a class of Auslander algebras

Abstract

Let $\Lambda$ be a radical square zero algebra of a Dynkin quiver and let $\Gamma$ be the Auslander algebra of $\Lambda$. Then the number of tilting right $\Gamma$-modules is $2^{m-1}$ if $\Lambda$ is of $A_m$ type for $m\ge 1$. Otherwise, the number of tilting right $\Gamma$-modules is $2^{m-3}\times 14$ if $\Lambda$ is either of $D_m$ type for $m\ge 4$ or of $E_m$ type for $m=6,7,8$.

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