Indecomposables with smaller cohomological length in the derived category of gentle algebras
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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.
Keywordscohomological length generalized string (band) derived discrete algebras
MSC(2010)16E05 16E10 16G20 18E30
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This work was supported by National Natural Science Foundation of China (Grant Nos. 11601098 and 11701321) and Science Technology Foundation of Guizhou Province (Grant Nos. 1038, 2036 and 5788). The author thanks Professor Yang Han, for the help and support during his visit in Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and also for discussions related to this paper.