{"paper":{"title":"Truncation and duality results for Hopf image algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Teodor Banica","submitted_at":"2014-04-14T11:39:24Z","abstract_excerpt":"Associated to an Hadamard matrix $H\\in M_N(\\mathbb C)$ is the spectral measure $\\mu\\in\\mathcal P[0,N]$ of the corresponding Hopf image algebra, $A=C(G)$ with $G\\subset S_N^+$. We study here a certain family of discrete measures $\\mu^r\\in\\mathcal P[0,N]$, coming from the idempotent state theory of $G$, which converge in Ces\\`aro limit to $\\mu$. Our main result is a duality formula of type $\\int_0^N(x/N)^pd\\mu^r(x)=\\int_0^N(x/N)^rd\\nu^p(x)$, where $\\mu^r,\\nu^r$ are the truncations of the spectral measures $\\mu,\\nu$ associated to $H,H^t$. We prove as well, using these truncations $\\mu^r,\\nu^r$, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3544","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}