A study of dimension 5 Ore extensions
In order to study AS-regular algebras of dimension 5, we consider dimension 5 graded iterated Ore extensions generated in degree one. We present an interesting example of an Ore extension with two generators and a degree type first discussed by Floystad and Vatne. We classify the possible degrees of relations and structure of the free resolution for extensions with 3 and 4 generators. We show that every known type of algebra of dimension 5 can be realized by an Ore extension and we consider which of these types cannot be realized by an enveloping algebra. We then investigate the possible bigrading of Ore extensions with degree types that cannot be realized by an enveloping algebra and show that there is no AS-regular algebra with minimal relations of degrees 2, 2, and 3.