5
votes
0answers
46 views

When are infinite dimensional path algebras hereditary

The title says mostly everything. Suppose we have a quiver, maybe with relations and cycles. Is it known when the path algebra modulo relations is hereditary. Especially in the case that the path ...
4
votes
1answer
99 views

When are path algebras of quivers hereditary.

Suppose we have a finite quiver with relations, possibly with oriented cycles. Is it known when the path algebra of this quiver (with relations) is hereditary?
3
votes
1answer
178 views

Projective indecomposables versus general indecomposables

Given a finite dimensional algebra, what is the exact relation between the indecomposable projective modules, and a general indecomposable module? In the case of an oriented quiver without cycles for ...
2
votes
1answer
210 views

Is every finitely dimensional basic $K$-algebra isomorphic to a bound quiver algebra?

Given a positive integer $n$, how to classify $n$-dimensional basic $K$-algebras?, where $K$ is algebraically closed. For $n=3$, Let $A=\left[ \begin{array}{ccc} ...
3
votes
1answer
169 views

how to find all simple modules for the given path algebra

Let $A = KQ$, where $Q$ is the quiver $$\begin{array}{ccc} & \alpha & \\ 1 & \rightleftarrows & 2 \\ & \beta& \end{array}$$ are there simple right $A$-modules with dimension ...
6
votes
1answer
212 views

how to get the injective envelope and projective cover of a given module

Given a bound quiver $(Q, I)$ and a representation $M$ of $Q$, how to get the injective envelope and projective cover of $M$? how to give the corresponding essential monomorphism and superfluous ...
2
votes
1answer
193 views

Given a quiver, how do you get the indecomposable injective modules from indecomposable projective modules?

Given a quiver, we know that it is easy to get the indecomposable projective modules, but the indecomposable injective modules are not easy to get. How do you get the indecomposable injective ...
3
votes
1answer
242 views

admissible ideals

How to prove the following conclusion : For any finite quiver $Q$, an ideal $I$ of $KQ$, contained in $R^2_Q$, is admissible if and only if, for each cycle $\sigma$ in $Q$, there exists $s \geq 1$ ...
1
vote
1answer
83 views

Is an abstract simplicial complex a quiver?

Let $\Delta$ be an abstract simplicial complex. Then for $B\in \Delta$ and $A\subseteq B$ we have that $A\in\Delta$. If we define $V$ to be the set of faces of $\Delta$, construct a directed edge from ...