On algebras of $\Omega^n$-finite and $\Omega^{\infty}$-infinite representation type
In this article we characterize the subcategory $\Omega^{\infty}(\mod A)$ for algebras of $\Omega^{n}$-finite representation type. As a consequence, we charaterize when a truncated path algebra is a Co-Gorenstein algebra in terms of its associated quiver. We also study the behaviour of Artin algebras of $\Omega^{\infty}$-infinite representation type. Finally, it is presented an example of a non Gorenstein algebra of $\Omega^{\infty}$-infinite representation type and an example of a finite dimensional algebra with infinite $\phi$-dimension.