Title: Chebyshev polynomials on symmetric matrices

Abstract: In this paper we evaluate  Chebyshev polynomials of the second-kind on a class of  
symmetric integer matrices, namely on adjacency matrices of simply                 
laced Dynkin and extended Dynkin diagrams. As an application of these results we   
explicitly calculate minimal projective resolutions of simple                      
modules of symmetric algebras with radical cube zero that are of                   
finite and tame representation type.