We introduce some new Frobenius subcategories of the module category of a preprojective algebra of Dynkin type, and we show that they have a cluster structure in the sense of Buan-Iyama-Reiten-Scott. These categorical cluster structures yield cluster algebra structures in the coordinate rings of intersections of opposed Schubert cells.
- Pub Date:
- February 2014
- Mathematics - Representation Theory;
- Mathematics - Rings and Algebras
- 31 pages, v.2 : a comment about the relation to Muller-Speyer conjecture on positroid varieties is added in 7.3. v.3. final version, to appear in Advances in Math