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

2016/09/15 by Zhang, Chao · 1 citation
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1609.04497

Abstract

Bongartz and Ringel 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 study this "no gaps" theorem for the bounded derived module category D^b(A) of a gentle algebra A: if there is an indecomposable object in D^b(A) of cohomological length l>1, then there exists an indecomposable with cohomological length l-1.

Cited by

• Homological Bounds of Gentle algebras

Related

• Indecomposables live in all smaller lengths
• Indecomposables live in all smaller lengths
• On compact exceptional objects in derived module categories
• The 1-periodic derived category of a gentle algebra : Part 1 -- Indecomposable objects
• On indecomposable exceptional modules over gentle algebras