We study possible connections between Rota-Baxter operators of non-zero weight and non-skew-symmetric solutions of the classical Yang-Baxter equation on finite-dimensional quadratic Lie algebras. The particular attention is made to the case when for a solution r the element r + r(r) is L-invariant.
- classical Yang-Baxter equation
- non-associative bialgebra
- quadratic Lie algebra
- Rota-Baxter operator
- 1.01 MATHEMATICS
State classification of scientific and technological information
- 27 MATHEMATICS