Minimal right determiners of irreducible morphisms in string algebras

Abstract

Let $\Lambda$ be a finite dimensional string algebra over a field with the quiver $Q$ such that the underlying graph of $Q$ is a tree, and let $|\Det(Λ)|$ be the number of the minimal right determiners of all irreducible morphisms between indecomposable left $\Lambda$-modules. Then we have $$|\Det(Λ)|=2n-p-q-1,$$ where $n$ is the number of vertices in $Q$, $p=|\{i\mid i$ is a source in $Q$ with two neighbours$\}|$ and $q$ is the number of non-zero vertex ideals of $\Lambda$.

18 pages. arXiv admin note: text overlap with arXiv:1608.07918

References in corpus (1)

• Minimal right determiners of irreducible morphisms in algebras of type ${\mathbb{A}}_n$