Reconstruction of path algebras from their posets of tilting modules

Happel, Dieter; Unger, Luise

doi:10.1090/S0002-9947-09-04644-3

Reconstruction of path algebras from their posets of tilting modules
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by Dieter Happel and Luise Unger PDF

Trans. Amer. Math. Soc. 361 (2009), 3633-3660 Request permission

Abstract:

Let $\Lambda = k \overrightarrow {\Delta }$ be the path algebra of a finite quiver without oriented cycles. The set of isomorphism classes of multiplicity free tilting modules is in a natural way a partially ordered set. We will show here that $\mathcal T_{\Lambda }$ uniquely determines $\overrightarrow {\Delta }$ if $\overrightarrow {\Delta }$ has no multiple arrows and no isolated vertices.

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