{"paper":{"title":"Cohomological Hall algebra of a symmetric quiver","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.AG","authors_text":"Alexander I. Efimov","submitted_at":"2011-03-14T18:38:40Z","abstract_excerpt":"In the paper \\cite{KS}, Kontsevich and Soibelman in particular associate to each finite quiver $Q$ with a set of vertices $I$ the so-called Cohomological Hall algebra $\\cH,$ which is $\\Z_{\\geq 0}^I$-graded. Its graded component $\\cH_{\\gamma}$ is defined as cohomology of Artin moduli stack of representations with dimension vector $\\gamma.$ The product comes from natural correspondences which parameterize extensions of representations. In the case of symmetric quiver, one can refine the grading to $\\Z_{\\geq 0}^I\\times\\Z,$ and modify the product by a sign to get a super-commutative algebra $(\\cH,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2736","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"}