caa a22 4500 467910561 CHVBK 20180406152848.0 cr unu---uuuuu 170328e20060201xx s 000 0 eng 10.1007/s11232-006-0016-6 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0016-6 Compatible Lie Brackets and the Yang-Baxter Equation [Elektronische Daten] [I. Golubchik, V. Sokolov] We show that any pair of compatible Lie brackets with a common invariant form produces a nonconstant solution of the classical Yang-Baxter equation. We describe the corresponding Poisson brackets, Manin triples, and Lie bialgebras. It turns out that all bialgebras associated with the solutions found by Belavin and Drinfeld are isomorphic to some bialgebras generated by our solutions. For any compatible pair, we construct a double with a common invariant form and find the corresponding solution of the quantum Yang-Baxter equation for this double. Springer Science+Business Media, Inc., 2006 Yang-Baxter equation nationallicence Lie bialgebra nationallicence Manin triple nationallicence Golubchik I. Bashkir State Pedagogical University, Ufa, Russia aut Sokolov V. Landau Institute for Theoretical Physics, RAS, Moscow, Russia aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 146/2(2006-02-01), 159-169 0040-5779 146:2<159 2006 146 11232 https://doi.org/10.1007/s11232-006-0016-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0016-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Golubchik I. Bashkir State Pedagogical University, Ufa, Russia aut NATIONALLICENCE 700 1- Sokolov V. Landau Institute for Theoretical Physics, RAS, Moscow, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 146/2(2006-02-01), 159-169 0040-5779 146:2<159 2006 146 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer