2016/07/26 by Ruipu Bai, Weiwei Guo, Bai, Ruipu +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1607.07913
openalex publication_date 2016/07/26 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
The n-Lie bialgebras are studied. In Section 2, the n-Lie coalgebra with rank r is defined, and the structure of it is discussed. In Section 3, the n-Lie bialgebra is introduced. A triple (L, μ, Δ) is an n-Lie bialgebra if and only if Δ is a conformal 1-cocycle on the n-Lie algebra L associated to L-modules (L⊗ n, ρsμ), 1≤ s≤ n, and the structure of n-Lie bialgebras is investigated by the structural constants. In Section 4, two-dimensional extension of finite dimensional n-Lie bialgebras are studied. For an m dimensional n-Lie bialgebra (L, μ, Δ), and an adμ-invariant symmetric bilinear form on L, the m+2 dimensional (n+1)-Lie bialgebra is constructed. In the last section, the bialgebra structure on the finite dimensional simple n-Lie algebra An is discussed. It is proved that only bialgebra structures on the simple n-Lie algebra An are rank zero, and rank two.