Mutation of torsion pairs in triangulated categories and its geometric realization

Details Mutation of torsion pairs in triangulated categories and its geometric realization Mutation of torsion pairs in triangulated categories and its geometric realization

2011-05-18

arxiv.org/abs/1105.3521v1

Mathematics

Representation Theory

20pages and 6 pictures

Scientific paper

By generalizing mutation of rigid subcategories, maximal rigid subcategories and cluster tilting subcategories, the notion of mutation of torsion pairs in triangulated categories is introduced. It is proved that the mutation of torsion pairs in triangulated categories are torsion pairs. It is also proved that there is no non-trivial mutation of t-structures, but shift. A geometric realization of mutation of torsion pairs in the cluster categories of type $A_n$ or in the cluster categories of type $A_{\infty}$ is given via the mutations (generalized flips) of Ptolemy diagrams of a regular $(n+3)-$gon $P_{n+3}$ or of a $\infty-$gon $P_{\infty}$ respectively.

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