MINIMAL REPRESENTATION-INFINITE COIL ALGEBRAS

For a basic and connected finite dimensional algebra A over an algebraically closed field, we study when the cycles in the category mod A (of finite dimensional modules) are well-behaved. We call A cycle-finite if, for any cycle in mod A, no morphism on the cycle lies in the infinite power of the radical. We show that, in this case, A is tame. We also introduce a natural generalisation of a tube, called a coil, and define A to be a coil algebra if any cycle in mod A lies in a standard coil. We prove that the minimal representation-infinite coil algebras coincide with the tame concealed algebras. © 1990 Springer-Verlag.