Ulrich Thiel, University of Kaiserslautern-Landau

Title: The rank one property for free Frobenius extensions

Abstract: The Cartan matrix of a finite-dimensional algebra is the matrix of multiplicities of simple modules in indecomposable projective modules. This is crucial information about the representation theory of the algebra. In my talk I will present a general setting including several important examples from Lie theory, such as restricted quantized enveloping algebras at roots of unity, in which we could prove that the Cartan matrix has the remarkable property of being blockwise of rank one. This is joint work with Gwyn Bellamy.