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We show that all four orbits of the unit space $\\mathcal{G}_{\\mathrm{tight}}^{(0)}$ under the natural action of $\\mathcal{G}_{\\mathrm{tight}}$ are locally closed, and that the associated isotropy groups are isomorphic to $\\mathbb{Z}$. Consequently, every irreducible representation of $C^*(\\mathcal{G}_{\\mathrm{tight}})$ is induced from an ir","authors_text":"Bipul Saurabh, Shreema Subhash Bhatt, Vinay Deshpande","cross_cats":[],"headline":"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.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-04-11T05:58:22Z","title":"$C(SO_q(4)/SO_q(2))$ as a Groupoid $C^*$-algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.10047","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-10T16:37:43.354027Z","id":"45e21694-ff02-4c9e-bde1-f85a5c298c74","model_set":{"reader":"grok-4.3"},"one_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.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"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.","strongest_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)).","weakest_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."}},"verdict_id":"45e21694-ff02-4c9e-bde1-f85a5c298c74"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:470a6dabd4f40b2d84597c9c1d6ec1f00231273928b510a4e654fbe2b4f673a1","target":"record","created_at":"2026-05-20T00:03:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"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}},"canonical_sha256":"1a16fac6b2d02f1e3cf91a8295aa0b056e2616f34fcecf7a8a58c403ff5464a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a16fac6b2d02f1e3cf91a8295aa0b056e2616f34fcecf7a8a58c403ff5464a0","first_computed_at":"2026-05-20T00:03:10.999806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:10.999806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4vg/g+s4cjXVZBQTj/QflQpB/5pRqNkzq4z6u++NBIX2BmMafXTtXprr1lNSJYhEW+Ae1CfyzYLlxk7ZIu+iCg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:11.000771Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.10047","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:470a6dabd4f40b2d84597c9c1d6ec1f00231273928b510a4e654fbe2b4f673a1","sha256:adff702250c74003841318f184779dfedc0f6b9c94ae53e39be5ca1e3e629f51"],"state_sha256":"229a11dea16d4e68f051d774b29076418670b9fcb80d76e7a36a50050ccc8d7e"}