LAUSR

Abstract Let A = K Q / I be a finite dimensional triangular K -algebra. Let ϕ A be the Coxeter matrix of A . We relate homological conditions for A with properties of the traces of the Coxeter transformation ϕ A . For instance, a finite dimensional accessible algebra A is strongly accessible if and only if Tr ( ϕ A ) = − 1 . We say A is of cyclotomic type if the eigenvalues of ϕ A lie on the unit circle. Clearly, if A is of cyclotomic type then | Tr ( ϕ A ) k | ≤ n , for k ≥ 0 . We prove that A is of cyclotomic type if | Tr ( ϕ A ) k | ≤ n holds for 0 ≤ k ≤ n . We illustrate the results with examples of Nakayama algebras.