2015/12/07 by Ruipu Bai, Yinghua Zhang, Bai, Ruipu +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1512.02261
16pages. arXiv admin note: text overlap with arXiv:1407.3159 by other authors
arxiv created 2015/12/07 · arxiv updated 2015/12/09
In the paper we study homogeneous Rota-Baxter operators with weight zero on the infinite dimensional simple 3-Lie algebra Aω over a field F ( ch F=0 ) which is realized by an associative commutative algebra A and a derivation Δ and an involution ω ( Lemma \mreflem:rbd3 ). A homogeneous Rota-Baxter operator on Aω is a linear map R of Aω satisfying R(Lm)=f(m)Lm for all generators of Aω, where f : Aω → F. We proved that R is a homogeneous Rota-Baxter operator on Aω if and only if R is the one of the five possibilities R01, R02,R03,R04 and R05, which are described in Theorem \mrefthm:thm1, \mrefthm:thm4, \mrefthm:thm01, \mrefthm:thm03 and \mrefthm:thm04. By the five homogeneous Rota-Baxter operators R0i, we construct new 3-Lie algebras (A, [ , , ]i) for 1≤ i≤ 5, such that R0i is the homogeneous Rota-Baxter operator on 3-Lie algebra (A, [ , , ]i), respectively.