{
  "id": "1009.3370",
  "version": "v3",
  "published": "2010-09-17T08:54:52.000Z",
  "updated": "2011-07-16T17:25:41.000Z",
  "title": "Silting mutation in triangulated categories",
  "authors": [
    "Takuma Aihara",
    "Osamu Iyama"
  ],
  "comment": "29 pages",
  "doi": "10.1112/jlms/jdr055",
  "categories": [
    "math.RT",
    "math.CT",
    "math.RA"
  ],
  "abstract": "In representation theory of algebras the notion of `mutation' often plays important roles, and two cases are well known, i.e. `cluster tilting mutation' and `exceptional mutation'. In this paper we focus on `tilting mutation', which has a disadvantage that it is often impossible, i.e. some of summands of a tilting object can not be replaced to get a new tilting object. The aim of this paper is to take away this disadvantage by introducing `silting mutation' for silting objects as a generalization of `tilting mutation'. We shall develope a basic theory of silting mutation. In particular, we introduce a partial order on the set of silting objects and establish the relationship with `silting mutation' by generalizing the theory of Riedtmann-Schofield and Happel-Unger. We show that iterated silting mutation act transitively on the set of silting objects for local, hereditary or canonical algebras. Finally we give a bijection between silting subcategories and certain t-structures.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-07-16T17:25:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triangulated categories",
      "silting mutation act",
      "silting objects",
      "plays important roles",
      "tilting object"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.3370A"
    }
  }
}