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Indecomposables with smaller cohomological length in the derived category of gentle algebras

Authors
  • Zhang, Chao
Type
Published Article
Journal
Science China Mathematics
Publisher
Science China Press
Publication Date
Nov 23, 2018
Volume
62
Issue
5
Pages
891–900
Identifiers
DOI: 10.1007/s11425-017-9270-x
Source
Springer Nature
Keywords
License
Yellow

Abstract

Bongartz (2013) and Ringel (2011) proved that there is no gaps in the sequence of lengths of indecomposable modules for the finite-dimensional algebras over algebraically closed fields. The present paper mainly studies this "no gaps" theorem as to cohomological length for the bounded derived category Db(A) of a gentle algebra A: if there is an indecomposable object in Db(A) of cohomological length l > 1, then there exists an indecomposable with cohomological length l-1.

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