Addendum and Erratum: Mapping cones for morphisms involving a band complex in the bounded derived category of a gentle algebraThanks: This work has been supported through the EPSRC grant EP/P016014/1 for the first named author and the EPSRC Early Career Fellowship EP/P016294/1 for the third named author.
İlke Çanakçi^∙ Address: Department of Mathematics, VU, Amsterdam, Amsterdam, 1081 HV, The Netherlands. Email address: , David Pauksztello Address: Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, United Kingdom Email address: and Sibylle Schroll Address: Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom. Email address:
Abstract
In this note we correct two oversights in [Mapping cones in the bounded derived category of a gentle algebra, J. Algebra 530 (2019), 163–194] which only occur when a band complex is involved. As a consequence we see that the mapping cone of a morphism between two band complexes can decompose into arbitrarily many indecomposable direct summands.
原文 arXiv:2001.06435;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2001.06435v1