• norsk
    • English
  • English 
    • norsk
    • English
  • Login
View Item 
  •   Home
  • Handelshøyskolen BI
  • Articles
  • Scientific articles
  • View Item
  •   Home
  • Handelshøyskolen BI
  • Articles
  • Scientific articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Iterated Extensions and Uniserial Length Categories

Eriksen, Eivind
Peer reviewed, Journal article
Published version
Thumbnail
View/Open
Eriksen2020_Article_IteratedExtensionsAndUniserial.pdf (351.2Kb)
URI
https://hdl.handle.net/11250/2835996
Date
2020
Metadata
Show full item record
Collections
  • Scientific articles [1722]
Original version
Algebras and Representation Theory. 2020, .   10.1007/s10468-020-09946-0
Abstract
In this paper, we study length categories using iterated extensions. We fix a field k, and for any family S of orthogonal k-rational points in an Abelian k-category A, we consider the category Ext(S) of iterated extensions of S in A, equipped with the natural forgetful functor Ext(S) → A(S) into the length category A(S). There is a necessary and sufficient condition for a length category to be uniserial, due to Gabriel, expressed in terms of the Gabriel quiver (or Ext-quiver) of the length category. Using Gabriel’s criterion, we give a complete classification of the indecomposable objects in A(S) when it is a uniserial length category. In particular, we prove that there is an bstruction for a path in the Gabriel quiver to give rise to an indecomposable object. The obstruction vanishes in the hereditary case, and can in general be expressed using matric Massey products. We discuss the close connection between this obstruction, and the noncommutative deformations of the family S in A. As an application, we classify all graded holonomic D-modules on a monomial curve over the complex numbers, obtaining the most explicit results over the affine line, when D is the first Weyl algebra. We also give a non-hereditary example, where we compute the obstructions and show that they do not vanish.
Journal
Algebras and Representation Theory

Contact Us | Send Feedback

Privacy policy
DSpace software copyright © 2002-2019  DuraSpace

Service from  Unit
 

 

Browse

ArchiveCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsDocument TypesJournalsThis CollectionBy Issue DateAuthorsTitlesSubjectsDocument TypesJournals

My Account

Login

Statistics

View Usage Statistics

Contact Us | Send Feedback

Privacy policy
DSpace software copyright © 2002-2019  DuraSpace

Service from  Unit