{\nu}-stable {\tau}-tilting modules
Abstract
Inspired by tau-tilting theory [AIR], we introduce the notion of nu-stable support tau-tilting modules. For any finite dimensional selfinjective algebra {\Lambda}, we give bijections between two-term tilting complexes in Kb(proj {\Lambda}), nu-stable support tau-tilting {\Lambda}-modules and nu-stable functorially finite torsion classes in mod {\Lambda}. Moreover, these objects correspond bijectively to selfinjective cluster tilting objects in C if {\Lambda} is a 2-CY tilted algebra associated with a Hom-finite 2-CY triangulated category C. As an application, we give a necessary condition such that selfinjective algebras are 2-CY tilted.
Cite
@article{arxiv.1210.8322,
title = {{\nu}-stable {\tau}-tilting modules},
author = {Yuya Mizuno},
journal= {arXiv preprint arXiv:1210.8322},
year = {2013}
}
Comments
12 pages. Typos are corrected. to appear in Comm. Algebra. arXiv admin note: text overlap with arXiv:1210.1036 by other authors