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Addendum and Erratum: Mapping cones for morphisms involving a band complex in the bounded derived category of a gentle algebra

Ilke Canakci, David Pauksztello, Sibylle Schroll

Published 2020-01-17Version 1

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, also arXiv:1609.09688] 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.

Comments: 13 pages, addendum and erratum to arXiv:1609.09688

Categories: math.RT, math.RA

Subjects: 18E30, 16G10, 05E10

Keywords: bounded derived category, band complex, mapping cone, gentle algebra, indecomposable direct summands

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