2017/08/09 by Sergio Chouhy · 11 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Associative property #Closure (psychology) #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Property (philosophy) #Space (punctuation) #Vector space #math.RA #msc:13D10
paper · pdf · doi:10.1112/blms.12277
published in Bulletin of the London Mathematical Society 51(5), 787-797 (Wiley) · 11 pages
arxiv created 2017/08/09 · openalex created_date 2017/08/17 · openalex publication_date 2019/07/24 · arxiv updated 2019/07/31 · openalex updated_date 2026/08/05
We study the degeneration relations on the varieties of associative and Lie algebra structures on a fixed finite-dimensional vector space and give a description of them in terms of Gerstenhaber formal deformations and quasi-affine lines. We use this result to show how the orbit closure of the three-dimensional Lie algebras can be determined using homological algebra. For the case of finite-dimensional associative algebras, we prove that the N-Koszul property is preserved under the degeneration relation for all N ⩾ 2 .