Representation types of the category of subprojective representations of a finite poset over K(t)/(t m ) and a solution of a Birkhoff type problem
By Daniel Simson. 2007
53 citations recorded by the source corpus.
We determine the representation type (wild, tame, polynomial growth) of the category fspr(I, Fm) of filtered subprojective Fm-representations of a finite poset I in terms of m and I ,w hereFm = K[t]/(t m ), m 1, and K is an algebraically closed field. Criteria for tameness, wildness and tameness of nonpolynomial growth of fspr(I, Fm) are given in Theorems 1.1 and 1.2. As an application, a solution of Birkhoff’s type problem [G. Birkhoff, Subgroups of abelian groups, Proc. London Math. Soc. 38 (1934) 385–401] for the category rep ft (I, Fm) of filtered I -chains of Fm-modules is given in Section 5, by determining the representation type repft(I, Fm). © 2007 Elsevier Inc. All rights reserved.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8eb0ef5aa63276f24652ec590388b52fe9640c05
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Monic representations and Gorenstein-projective modules (2011, background): “Schmidmeier [2006; 2008a; 2008b]; see also [Simson 2007].”
- Triangle singularities, ADE-chains, and weighted projective lines (2012, background): “Another, quite surprising, application concerns the invariant subspace problem for nilpotent operators, a subject intensively studied by Ringel and Schmidmeier [66]; we also refer to related work by Simson [68] and Pu Zhang [73].”