{"paper":{"title":"The spectra of lifted digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Dalf\\'o, J. \\v{S}ir\\'a\\v{n}, M. A. Fiol","submitted_at":"2017-07-14T11:19:43Z","abstract_excerpt":"We present a method to derive the complete spectrum of the lift $\\Gamma^\\alpha$ of a base digraph $\\Gamma$, with voltage assignments on a (finite) group $G$. The method is based on assigning to $\\Gamma$ a quotient-like matrix whose entries are elements of the group algebra $\\mathbb{C}[G]$, which fully represents $\\Gamma^{\\alpha}$. This allows us to derive the eigenvectors and eigenvalues of the lift in terms of those of the base digraph and the irreducible characters of $G$. Thus, our main theorem generalize some previous results of Lov\\'az and Babai concerning the spectra of Cayley digraphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04463","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":""},"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"}