{
  "annotation_id": "8f473b91-e697-4293-8f17-14c44aade4a2",
  "date_created": "2026-02-17T05:53:12.431000Z",
  "date_modified": "2026-02-17T05:53:12.431000Z",
  "file_hash": "028a37839db31eea88e7ac1d0af356546dd0efcfeb5dc70b40f6b16c85d1e070",
  "private": false,
  "record": {
    "abstract": "We characterise stable finiteness and pure infiniteness of the essential crossed product of a C*-algebra by an action of an inverse semigroup. Under additional assumptions, we prove a stably finite / purely infinite dichotomy. Our main technique is the development, using an induced action, of a \u0027\u0027dynamical Cuntz semigroup\u0027\u0027 that is a subquotient of the usual Cuntz semigroup. We prove that the essential crossed product is stably finite / purely infinite if and only if the dynamical Cuntz semigroup admits / does not admit a nontrivial state. Indeed, a retract of our dynamical Cuntz semigroup suffices to prove the dichotomy. Our results generalise those by Rainone on crossed products of groups acting by automorphisms of a C*-algebra, and we recover results by Kwa\\\u0027sniewski--Meyer--Prasad on C*-algebras of non-Hausdorff groupoids.",
    "arxiv_id": "2601.07100",
    "authors": [
      "Becky Armstrong",
      "Lisa Orloff Clark",
      "Astrid An Huef",
      "Diego Mart\u00ednez",
      "Ilija Tolich"
    ],
    "categories": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "A Dichotomy for Inverse-Semigroup Crossed Products via Dynamical Cuntz Semigroups",
    "url": "https://arxiv.org/abs/2601.07100",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fd93179a-eec8-4875-8362-da21b3778123",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}