{"paper":{"title":"*-Structures on Module-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Matthew Tucker-Simmons","submitted_at":"2012-11-28T16:49:55Z","abstract_excerpt":"This chapter lays out a framework for discussing (\\ast)-structures on module-algebras over a Hopf (\\ast)-algebra (H). We define a complex conjugation functor (V \\mapsto \\bar{V}), which is an involution on the module category (\\hmod), and discuss its interaction with natural constructions such as direct sums, duality, Hom, and tensor products. We define (\\ast)-structures first at the level of modules. We say that (V) is a (\\ast)-module if there is an isomorphism (\\ast : \\bar{V} \\to V) in (\\hmod) which is involutive in an appropriate sense. Then we define (\\ast)-structures on algebras in (\\hmod)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6652","kind":"arxiv","version":2},"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"}