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

  • Steffen Koenig

    Universität Stuttgart Department of Mathematics Institut für Algebra Nanjing University und Zahlentheorie Nanjing 210093 Pfaffenwaldring 57 P. R. China D-70569 Stuttgart
  • Dong Yang

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

Bijective correspondences are established between (1) silting objects, (2) simple-minded collections, (3) bounded -structures with length heart and (4) bounded co--structures. These correspondences are shown to commute with mutations and partial orders. The results are valid for finite-dimensional algebras. A concrete example is given to illustrate how these correspondences help to compute the space of Bridgeland's stability conditions.

Cite this article

Steffen Koenig, Dong Yang, Silting objects, simple-minded collections, -structures and co--structures for finite-dimensional algebras. Doc. Math. 19 (2014), pp. 403–438

DOI 10.4171/DM/451