2016/05/07 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.1605.02252
17 pages
arxiv created 2016/09/26 · arxiv updated 2016/09/28
In this paper we study k-order homogeneous Rota-Baxter operators with weight 1 on the simple 3-Lie algebra Aω (over a field of characteristic zero), which is realized by an associative commutative algebra A and a derivation Δ and an involution ω (Lemma \mreflem:rbd3). A k-order homogeneous Rota-Baxter operator on Aω is a linear map R satisfying R(Lm)=f(m+k)Lm+k for all generators \ Lm~ |~ m∈ \mathbb Z \ of Aω and a map f : \mathbb Z →\mathbb F, where k∈ \mathbb Z. We prove that R is a k-order homogeneous Rota-Baxter operator on Aω of weight 1 with k≠ 0 if and only if R=0 (see Theorems 3.2, and R is a 0-order homogeneous Rota-Baxter operator on Aω of weight 1 if and only if R is one of the forty possibilities which are described in Theorems3.5, 3.7, 3.9, 3.10, 3.18, 3.21 and 3.22.