Pith Number

pith:ZDNWCHE4

pith:2026:ZDNWCHE4MZOHN4QMGJRJFFLDOW

not attested not anchored not stored refs resolved

Are cluster automorphism groups finitely generated?

Changjian Fu, Yinzhi Wang, Zhanhong Liang

A pseudo N-grading supplies a sufficient condition that makes cluster automorphism groups finitely generated.

arxiv:2605.16854 v1 · 2026-05-16 · math.RA · math.GR

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Claims

C1strongest claim

By applying the pseudo N-grading introduced in our previous work, we establish a sufficient condition for a cluster automorphism group to be finitely generated. As applications, we verify the finite generation of the automorphism groups for all finite mutation and acyclic cluster algebras.

C2weakest assumption

The pseudo N-grading defined in the authors' prior work is well-defined on the relevant cluster automorphism groups and satisfies the technical properties needed to imply finite generation.

C3one line summary

A sufficient condition based on pseudo N-grading proves that automorphism groups of finite-mutation and acyclic cluster algebras are finitely generated.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] Cluster automorphisms.Proceeding of the Lon- don Mathematical Society, 104(6):1271–1302, 2012 2012

[2] Unistructurality of cluster algebras of type ˜A.J 2016

[3] Unistructurality of cluster algebras from unpunctured surfaces.Proc 2020

[4] Automorphisms of cluster algebras of rank 2.Transformation Groups, 20(1):1–20, 2015 2015

[5] Quadratic differentials as stability conditions.Publ 2015

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:26.381882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8db611c9c665c76f20c326292956375b463456ea49d39bd878de8ce0eeefe08

Aliases

arxiv: 2605.16854 · arxiv_version: 2605.16854v1 · doi: 10.48550/arxiv.2605.16854 · pith_short_12: ZDNWCHE4MZOH · pith_short_16: ZDNWCHE4MZOHN4QM · pith_short_8: ZDNWCHE4

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZDNWCHE4MZOHN4QMGJRJFFLDOW \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c8db611c9c665c76f20c326292956375b463456ea49d39bd878de8ce0eeefe08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "396abb18fd2e71499a093d9213548e50acbcb5564bd80d7b3eb4fbc856d6f97f",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2026-05-16T07:39:17Z",
    "title_canon_sha256": "282465efc101346b5886fbd33492c9e18f48d98517f0e56cc34e2909bfbad302"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16854",
    "kind": "arxiv",
    "version": 1
  }
}