{"paper":{"title":"A \"q-deformed\" generalization of the Hosszu-Gluskin theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GR","math.MP","math.QA"],"primary_cat":"math.RA","authors_text":"Steven Duplij (Mathematical Institute, University of Muenster)","submitted_at":"2013-09-04T18:50:19Z","abstract_excerpt":"In this paper a new form of the Hossz\\'u-Gluskin theorem is presented in terms of polyadic powers and using the language of diagrams. It is shown that the Hossz\\'u-Gluskin chain formula is not unique and can be generalized (\"deformed\") using a parameter q which takes special integer values. A version of the \"q-deformed\" analog of the Hossz\\'u-Gluskin theorem in the form of an invariance is formulated, and some examples are considered. The \"q-deformed\" homomorphism theorem is also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1134","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"}