Classification of higher wide subcategories for higher Auslander algebras of type A

Abstract

A subcategory W of an abelian category is called wide if it is closed under kernels, cokernels , and extensions. Wide subcategories are of interest in representation theory because of their links to other homological and combinatorial objects, established among others by Ingalls–Thomas and Marks–Šťovíček. If d ⩾ 1 is an integer, then Jasso introduced the notion of d -abelian categories, where kernels, cokernels, and extensions have been replaced by longer complexes. Wide subcategories can be generalised to this situation. Important examples of d -abelian categories arise as the d -cluster tilting subcategories M n , d of mod A n d − 1 , where A n d − 1 is a higher Auslander algebra of type A in the sense of Iyama. This paper gives a combinatorial description of the wide subcategories of M n , d in terms of what we call non-interlacing collections.