{"paper":{"title":"Twisted $\\Gamma$-Lie algebras and their vertex operator representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fulin Chen, Qing Wang, Shaobin Tan","submitted_at":"2013-10-18T12:11:46Z","abstract_excerpt":"Let $\\Gamma$ be a generic subgroup of the multiplicative group $\\mathbb{C}^*$ of nonzero complex numbers. We define a class of Lie algebras associated to $\\Gamma$, called twisted $\\Gamma$-Lie algebras, which is a natural generalization of the twisted affine Lie algebras. Starting from an arbitrary even sublattice $Q$ of $\\mathbb Z^N$ and an arbitrary finite order isometry of $\\mathbb Z^N$ preserving $Q$, we construct a family of twisted $\\Gamma$-vertex operators acting on generalized Fock spaces which afford irreducible representations for certain twisted $\\Gamma$-Lie algebras. As application,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4985","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"}