{"paper":{"title":"Units of $\\mathbb{Z}/p\\mathbb{Z}$-equivariant $K$-theory and bundles of UHF-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.AT","authors_text":"Ulrich Pennig, Valerio Bianchi","submitted_at":"2024-10-09T14:45:02Z","abstract_excerpt":"We consider infinite tensor product actions of $G = \\mathbb{Z}/p\\mathbb{Z}$ on the UHF-algebra $D = \\text{End}(V)^{\\otimes \\infty}$ for a finite-dimensional unitary $G$-representation $V$ and determine the equivariant homotopy type of the group $\\text{Aut}(D \\otimes \\mathbb{K})$, where $\\mathbb{K}$ are the compact operators on $\\ell^2(G) \\otimes H_0$ for a separable Hilbert space $H_0$ with $\\dim(H_0) = \\infty$. We show that this group carries an equivariant infinite loop space structure revealing it as the first space of a naive $G$-spectrum, which we prove to be equivalent to the positive un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.06947","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.06947/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}