Quasi-hereditary algebras with two simple modules and fibonacci numbers

Let K be an algebraically closed field. In 10] Happel showed that number-theoretic properties of the Fibonacci numbers are related to ho-mological properties of a family of finite-dimensional Ji-algebras An. In particular he showed that at least for n > 3 odd, An is not derived equiv alent to a quasi-hereditary algebra.Using well-known properties that are shared by two rings that are derived equivalent and deeper properties of the Fibonacci numbers we are able to show that for all n > 3, the algebra A_n is not derived equivalent to a quasi-hereditary algebra.