Structure Theorems for Basic Algebras

Details Structure Theorems for Basic Algebras Structure Theorems for Basic Algebras

2011-02-05

arxiv.org/abs/1102.1100v1

Mathematics

Representation Theory

Scientific paper

A basic finite dimensional algebra over an algebraically closed field $k$ is isomorphic to a quotient of a tensor algebra by an admissible ideal. The category of left modules over the algebra is isomorphic to the category of representations of a finite quiver with relations. In this article we will remove the assumption that $k$ is algebraically closed to look at both perfect and non-perfect fields. We will introduce the notion of species with relations to describe the category of left modules over such algebras. If the field is not perfect, then the algebra is isomorphic to a quotient of a tensor algebra by an ideal that is no longer admissible in general. This gives hereditary algebras isomorphic to a quotient of a tensor algebra by a non-zero ideal. We will show that these non-zero ideals correspond to cyclic subgraphs of the graph associated to the species of the algebra. This will lead to the ideal being zero in the case when the underlying graph of the algebra is a tree.

Affiliated with

Also associated with

No associations

Rating

Structure Theorems for Basic Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Structure Theorems for Basic Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Structure Theorems for Basic Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-505805