2010/07/30 by David Khudaverdyan, Khudaverdyan, David, Ashis Kumar Mandal +4 · 1 citation
Mathematics · #17B70 #18D05 #18D10 #18G30 #55U15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.CT #math.QA #msc:17B70 #msc:18D05 #msc:18D10 #msc:18G30 #msc:55U15
paper · pdf · doi:10.48550/arxiv.1007.5458
21 pages, 1 figure
openalex publication_date 2010/07/30 · arxiv created 2011/06/16 · arxiv updated 2011/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define Lie 3-algebras and prove that these are in 1-to-1 correspondence with the 3-term Lie infinity algebras whose bilinear and trilinear maps vanish in degree (1,1) and in total degree 1, respectively. Further, we give an answer to a question of [Roy07] pertaining to the use of the nerve and normalization functors in the study of the relationship between categorified algebras and truncated sh algebras.