Pointed Brauer Trees

In this paper we establish a one-to-one correspondence between Brauer trees with an additional structure that we call “pointing” and equivalence classes of tilting complexes of the corresponding Brauer star algebra which are of a special “combinatorial” nature. Under the correspondence, the identification of the indecomposable summands of the tilting complex with edges of the Brauer tree is completely natural. The procedure gives an algorithm for producing large numbers of distinct tilting complexes for the same Brauer tree.