Two Sided Tilting Complexes for Green Orders and Brauer Tree Algebras Original Research Article

We give an explicit two sided tilting complex between two Green orders having the same structural data as they were defined by K. W. Roggenkamp. (1992,Comm. Algebra20, 1715–1734; and 1994,in“Finite Dimensional Algebras and Related Topics,” pp. 265–276, Kluwer Academic, Dordrecht/Norwell, MA). This yields an explicit two sided tilting complex between two Brauer tree algebras over the same field associated to trees with the same number of edges and the same exceptional multiplicity. The present work also gives a certain generalization of a result of Gabriel and Riedtmann (1979,Comment. Math. Helv.54, 240–287).