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Understanding Finite Dimensional Representations Generically

  • K. R. Goodearl
  • B. Huisgen-ZimmermannEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 242)

Abstract

We survey the development and status quo of a subject best described as “generic representation theory of finite dimensional algebras”, which started taking shape in the early 1980s. Let \({\Lambda }\) be a finite dimensional algebra over an algebraically closed field. Roughly, the theory aims at (a) pinning down the irreducible components of the standard parametrizing varieties for the \({\Lambda }\)-modules with a fixed dimension vector, and (b) assembling generic information on the modules in each individual component, that is, assembling data shared by all modules in a dense open subset of that component. We present an overview of results spanning the spectrum from hereditary algebras through the tame non-hereditary case to wild non-hereditary algebras.

Keywords

Varieties of representations Irreducible components Generic properties of representations 

2010 Mathematics Subject Classification

Primary 16G10 secondary 16G20 14M99 14M15 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA

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