Combinatorial partial tilting complexes for the Brauer star algebras (Q2782439)

Let \(A\) be a Brauer tree algebra over an algebraically closed field \(k\) associated to a star with \(e\) edges and with exceptional vertex of multiplicity \(m\) in the center. The authors study tilting complexes over \(A\) whose indecomposable direct factors are of length 1 or 2. The authors establish combinatorial criteria in order to classify the tilting complexes of this type over \(A\). The criteria are analogous to the one used by \textit{S. König} and the reviewer to classify two-sided tilting complexes for hereditary orders [Commun. Algebra 24, No. 6, 1897-1913 (1996; Zbl 0851.16012)]. The reason for this behaviour is that the Brauer star algebra \(A\) is the image of a Green order \(\Lambda\) defined by \textit{K. W. Roggenkamp} [in Commun. Algebra 20, No. 6, 1715-1734 (1992; Zbl 0748.20006)], and that this Green order essentially is built from a hereditary order. Moreover, there is a unique lift of a tilting complex over \(A\) to a tilting complex over \(\Lambda\) as proved by \textit{J. Rickard} [in J. Algebra 142, No. 2, 383-393 (1991; Zbl 0799.16014)].NEWLINENEWLINEFor the entire collection see [Zbl 0974.00038].