Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras

Details Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras

2012-03-26

arxiv.org/abs/1203.5657v2

Mathematics

Representation Theory

This incorporates arXiv:1011.3938. Typos corrected, remarks, references and citations added

Scientific paper

Bijective correspondences are established between (1) silting objects, (2) simple-minded collections, (3) bounded $t$-structures with length heart and (4) bounded co-$t$-structures. These correspondences are shown to commute with mutations. The results are valid for finite-dimensional non-positive differential graded algebras, in particular for finite dimensional algebras. Among the applications is a construction of bounded $t$-structures with piecewise hereditary hearts.

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