摘要
Bongartz(2013) and Ringel(2011) proved that there is no gaps in the sequence of lengths of indecomposable modules for the ?nite-dimensional algebras over algebraically closed ?elds. 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 D^b(A) of cohomological length l > 1, then there exists an indecomposable with cohomological length l-1.
Bongartz(2013) and Ringel(2011) proved that there is no gaps in the sequence of lengths of indecomposable modules for the ?nite-dimensional algebras over algebraically closed ?elds. 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 D^b(A) of cohomological length l > 1, then there exists an indecomposable with cohomological length l-1.
基金
supported by National Natural Science Foundation of China (Grant Nos. 11601098 and 11701321)
Science Technology Foundation of Guizhou Province (Grant Nos. [2016]1038, [2015]2036 and [2017]5788)
