On a Triangulated Category Which Behaves like a Cluster Category of Infinite Dynkin Type, and the Relation to Triangulations of the Infinity-gon
نویسندگان
چکیده
By a triangulation of the ∞-gon, we mean a maximal set of non-intersecting arcs connecting non-neighbouring integers: We adopt the philosophy that the integers can be viewed as the vertices of the ∞-gon, and that the arcs can be viewed as diagonals. There are two obvious ways to achieve such maximal sets; they are shown in the following two sketches where the arcs must be continued ad infinitum according to the indicated pattern. First a ‘leapfrog’ configuration which is locally
منابع مشابه
On a Cluster Category of Infinite Dynkin Type, and the Relation to Triangulations of the Infinity-gon
Let k be a field and let D be a k-linear algebraic triangulated category with split idempotents. Let Σ be the suspension functor of D and let s be a 2-spherical object of D, that is, the morphism space D(s,Σs) is k for i = 0 and i = 2 and vanishes otherwise. Assume that s classically generates D, that is, each object of D can be built from s using (de)suspensions, direct sums, direct summands, ...
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