The extension of Rota-Baxter Lie algebras. (Chinese. English summary) Zbl 1363.17009
Summary: The one-dimensional extension problem of Rota-Baxter Lie algebras is mainly concerned. The necessary and sufficient condition under which one-dimensional extension of a Rota-Baxter Lie algebra \((L,P)\) is a Rota-Baxter 3-Lie algebra \((A,Q)\) is given. Three kinds of 3-Lie multiplications \([,,]_1,[,,]_2\) and \([,,]_3\) on a one dimensional extension \(A\) of a vector space \(L\) are provided. It is shown that \((A,[,,]_3,Q)\) is a Rota-Baxter 3-Lie algebra with weight zero.
MSC:
| 17B05 | Structure theory for Lie algebras and superalgebras |
| 17A42 | Other \(n\)-ary compositions \((n \ge 3)\) |
