Infinite Dimensional Representations of Canonical Algebras

By I. Reiten, Claus Michael Ringel. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2002

60 citations recorded by the source corpus.

Abstract The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with canonical algebras. The investigation is centered around the generic and the Prüfer modules, and how other modules are determined by these modules.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d988d8f708fc72bcef11172ebf9f6da0fc44cdd9

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In Algebra and Number Theory

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Citations in the corpus

Recollements and tilting objects (2009, background): “It is shown in [34] thatW can be chosen as the direct sum of a set of representatives of the Prüfer R-modules and the generic R-module G.”
Definable Additive Categories: Purity and Model Theory (2011, unknown): “Various related examples of definable subcategories may be found in [98], [65] and [97].”
The telescope conjecture for hereditary rings via Ext-orthogonal pairs (2008, background): “The next example(1) arises from the work of Reiten and Ringel on infinite dimensional representations of canonical algebras; see [29] which is our reference for all concepts and results in the following discussion.”
Silting modules (2014, background): “For details on infinite di mensional modules over hereditary algebras we refer to [38, 37].”