2015/12/21 by Ruipu Bai, LI Qiyong, Bai, Ruipu +5 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #17B05 #17B30 #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Centralizer and normalizer #FOS: Mathematics #FOS: Physical sciences #Lie algebra #Mathematical Physics (math-ph) #Mathematics #Pure mathematics #Rings and Algebras (math.RA) #Sphingolipid Metabolism and Signaling #Universal enveloping algebra #math-ph #math.MP #math.RA #msc:17B05 #msc:17B30
paper · pdf · doi:10.48550/arxiv.1601.05345
published in arXiv (Cornell University) (Cornell University) · 19 pages. arXiv admin note: text overlap with arXiv:0805.1202 by other authors
arxiv created 2015/12/21 · openalex publication_date 2015/12/21 · arxiv updated 2016/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Generalized derivations, quasiderivations and quasicentroid of 3-algebras are introduced, and basic relations between them are studied. Structures of quasiderivations and quasicentroid of 3-Lie algebras, which contains a maximal diagonalized tours, are systematically investigated. The main results are: for all 3-Lie algebra A, 1) the generalized derivation algebra GDer(A) is the sum of quasiderivation algebra QDer(A) and quasicentroid QΓ(A); 2) quasiderivations of A can be embedded as derivations in a larger algebra; 3) quasiderivation algebra QDer(A) normalizer quasicentroid, that is, [QDer(A), QΓ(A)]⊆ QΓ(A); 4) if A contains a maximal diagonalized tours T, then QDer(A) and QΓ(A) are diagonalized T-modules, that is, as T-modules, (T, T) semi-simplely acts on QDer(A) and QΓ(A), respectively.