Pith Number

pith:DILPVRVS

pith:2026:DILPVRVS2AXR4PHZDKBJLKQLAV

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$C(SO_q(4)/SO_q(2))$ as a Groupoid $C^*$-algebra

Bipul Saurabh, Shreema Subhash Bhatt, Vinay Deshpande

The C*-algebra of the quantum homogeneous space SO_q(4)/SO_q(2) equals the C*-algebra of a tight groupoid built from the classical inverse semigroup.

arxiv:2604.10047 v3 · 2026-04-11 · math.OA

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Claims

C1strongest claim

We prove that C(SO_q(4)/SO_q(2)) is isomorphic to the C*-algebra of the tight groupoid G_tight associated with the inverse semigroup generated by the standard generators of its classical limit C(SO_0(4)/SO_0(2)). ... every irreducible representation of C*(G_tight) is induced from an irreducible representation of C*(Z) ... we explicitly construct their equivalence with the corresponding Soibelman irreducible representations of C(SO_q(4)/SO_q(2)).

C2weakest assumption

That the inverse semigroup generated by the standard generators of the classical limit C(SO_0(4)/SO_0(2)) produces a tight groupoid whose C*-algebra is exactly the quantum one, and that the four orbits are locally closed with isotropy groups precisely Z, allowing the induction and equivalence to Soibelman representations to hold without additional relations or exceptions.

C3one line summary

C(SO_q(4)/SO_q(2)) is isomorphic to C*(G_tight) for the tight groupoid from the classical inverse semigroup, with all irreps induced from C*(Z) and explicitly equivalent to Soibelman's representations.

Receipt and verification

First computed	2026-05-20T00:03:10.999806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a16fac6b2d02f1e3cf91a8295aa0b056e2616f34fcecf7a8a58c403ff5464a0

Aliases

arxiv: 2604.10047 · arxiv_version: 2604.10047v3 · doi: 10.48550/arxiv.2604.10047 · pith_short_12: DILPVRVS2AXR · pith_short_16: DILPVRVS2AXR4PHZ · pith_short_8: DILPVRVS

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DILPVRVS2AXR4PHZDKBJLKQLAV \
  | 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: 1a16fac6b2d02f1e3cf91a8295aa0b056e2616f34fcecf7a8a58c403ff5464a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a3d9b0552fade264a8c0f6627522f25124921ca1e063a6996cb3c3115c542bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-04-11T05:58:22Z",
    "title_canon_sha256": "77cf549c2c10cdc5adb30c8ce2f8de7988dc0e3f1e4a0fbe823ff3211c0a27cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.10047",
    "kind": "arxiv",
    "version": 3
  }
}