{"paper":{"title":"Cohomology and Deformations of Hom-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.RA","authors_text":"Abdenacer Makhlouf, Faouzi Ammar, Zeyneb Ejbehi","submitted_at":"2010-05-04T07:42:53Z","abstract_excerpt":"The purpose of this paper is to define  cohomology structures on Hom-associative algebras and Hom-Lie algebras. The first and second coboundary maps were  introduced by Makhlouf and Silvestrov in the study of one-parameter formal  deformations theory. Among  the relevant formulas for a generalization of Hochschild cohomology for Hom-associative algebras and  a Chevalley-Eilenberg cohomology for  Hom-Lie algebras, we define  Gerstenhaber bracket on the space of multilinear mappings of Hom-associative algebras and  Nijenhuis-Richardson bracket on the space of multilinear mappings of Hom-Lie alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0456","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"}