2021/05/28 by Erik Mainellis, Mainellis, Erik
Mathematics · #17A01 #17A30 #17A32 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2105.13969
openalex publication_date 2021/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a pair of nilpotent Lie algebras A and B, an extension 0\xrightarrow A\xrightarrow L\xrightarrow B\xrightarrow 0 is not necessarily nilpotent. However, if L1 and L2 are extensions which correspond to lifts of a map Φ:B\xrightarrow Out(A), it has been shown that L1 is nilpotent if and only if L2 is nilpotent. In the present paper, we prove analogues of this result for the algebras of Loday. As an important consequence, we thereby gain its associative analogue as a special case of diassociative algebras.