Maps between representations of zero-relation algebras
Let \(A=kQ/I\) be a zero-relation \(k\)-algebra over a field \(k\), \(R=k\widetilde Q/\widetilde I\) the universal Galois covering of \(A\) and \(F_\lambda:\text{mod\,}R\to\text{mod\,}A\) the associated push-down functor between the categories of finite-dimensional right modules. Then \(\widetilde Q\) is a locally finite tree and \(\widetilde I\) is generated by paths in \(\widetilde Q\). For a finite subtree \(S\) of \(\widetilde Q\) which does not contain subpaths from \(\widetilde I\), denote by \(V_ S\) the unique \(R\)-module (\(k\)-representation of \((\widetilde Q,\widetilde I)\)) which is one dimensional at each vertex of \(S\) and in which the linear maps corresponding to each arrow of \(S\) are the identity. The modules of the form \(F_\lambda V_S\) are called tree modules over \(A\). The author describes a basis for the space of homomorphisms between two tree modules.
categories of finite-dimensional right modules
scientific article; zbMATH DE number 4122164
scientific article