Commutative algebras of rational function matrices as endomorphisms of Kronecker modules. II.
A Kronecker module is a pair of modules \(U\) and \(V\) together with two homomorphisms from \(U\) to \(V\). The authors study the endomorphism algebras of indecomposable Kronecker modules over an algebraically closed field \(K\) which are extensions of finite dimensional torsion-free rank 1 modules by infinite dimensional torsion-free rank 1 modules. The infinite dimensional rank 1 module in the extension is characterized by a height function, a function which maps the elements of \(K\) and infinity to a non-negative integer or infinity. The authors prove that if the height function is constant infinity and the characteristic of the ground field \(K\) is not 2 then the endomorphism algebra is just \(K\). For other height functions, see part I [the authors, Linear Algebra Appl. 374, 41-62 (2003; see the review Zbl 1044.16022 above)].
scientific article; zbMATH DE number 2005993
scientific article