INDECOMPOSABLE OBJECTS DETERMINED BY THEIR INDEX IN HIGHER HOMOLOGICAL ALGEBRA

Let C be a 2-Calabi-Yau triangulated category, and let T be a cluster tilting subcategory of C. An important result from Dehy and Keller tells us that a rigid object c. C is uniquely defined by its index with respect to T. The notion of triangulated categories extends to the notion of (d + 2)-angulated categories. Thanks to a paper by Oppermann and Thomas, we now have a definition for cluster tilting subcategories in higher dimensions. This paper proves that under a technical assumption, an indecomposable object in a (d+ 2)-angulated category is uniquely defined by its index with respect to a higher dimensional cluster tilting subcategory. We also demonstrate that this result applies to higher dimensional cluster categories of Dynkin-type A.