Pith Number

pith:ILBHXVMI

pith:2026:ILBHXVMIOI74OFTFPUMQRHQEXZ

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Homological properties of simple modules over Leavitt path algebras

Alberto Tonolo, Francesca Mantese

Simple modules over Leavitt path algebras associated to cycles and irreducible polynomials have explicitly constructed projective resolutions, from which the dimensions of their extension spaces are computed.

arxiv:2604.11241 v2 · 2026-04-13 · math.RA

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\pithnumber{ILBHXVMIOI74OFTFPUMQRHQEXZ}

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Record completeness

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We explicitly construct the projective resolution of simple left modules over the Leavitt path algebra L_K(E) associated to cycles and irreducible polynomials. Then we study the dimension of the K-vector space of the extensions between two such simple modules.

C2weakest assumption

The explicitness of the resolutions and the resulting dimension formulas hold for arbitrary graphs E and any field K, without additional restrictions on the cycles or polynomials that would invalidate the constructions.

C3one line summary

Explicit projective resolutions are built for simple modules over Leavitt path algebras tied to cycles and irreducible polynomials, followed by computation of extension dimensions between them.

Receipt and verification

First computed	2026-05-22T01:04:02.043484Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42c27bd588723fc716657d19089e04be510d8fd125cc55e109e597cb1ac47fb2

Aliases

arxiv: 2604.11241 · arxiv_version: 2604.11241v2 · doi: 10.48550/arxiv.2604.11241 · pith_short_12: ILBHXVMIOI74 · pith_short_16: ILBHXVMIOI74OFTF · pith_short_8: ILBHXVMI

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ILBHXVMIOI74OFTFPUMQRHQEXZ \
  | 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: 42c27bd588723fc716657d19089e04be510d8fd125cc55e109e597cb1ac47fb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e06aea3f4e6b0336e97f379a3bd3e9506b12ee9e133466eca8f28ddef1e9b58",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2026-04-13T09:47:32Z",
    "title_canon_sha256": "86a91165b786db6fab4e8ed769cfc77e38e453a35e0ccc277c7201adc777f7c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.11241",
    "kind": "arxiv",
    "version": 2
  }
}