Kronecker modules generated by modules of length 2

2016/12/22 by Ringel, Claus Michael
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1612.07679

Abstract

Let Λ be a ring and \mathcal N a class of Λ-modules. A Λ-module is said to be generated by \mathcal N provided that it is a factor module of a direct sum of modules in \mathcal N. The semi-simple Λ-modules are just the Λ-modules which are generated by the Λ-modules of length 1. It seems that the modules which are generated by the modules of length 2 (we call them bristled modules) have not attracted the interest they deserve. In this paper we deal with the basic case of the Kronecker modules, these are the (finite-dimensional) representations of an n-Kronecker quiver, where n is a natural number. We show that for n≥ 3, there is an abundance of bristled Kronecker modules.

Related

• The elementary 3-Kronecker modules
• Combinatorial aspects of extensions of Kronecker modules
• Dimension vectors of elementary modules of generalized Kronecker quivers
• Decomposition theory of modules: the case of Kronecker algebra
• Indecomposable representations of the Kronecker quivers