The notion of compatible R-matrices was introduced by Isaev-Ogievetsky-Pyatov.
It enables one to introduced a large family of new quantum algebras and the
corresponding Bethe subalgebras. Also, this notion is useful for defining
the so-called half-quantum algebras (Isaev-Ogievetsky) which generalize the
notions of the Manin and q-Manin matrices. In my talk I plan to introduce all
these objects and to exhibit the role of the mentioned algebras in
studying the Yangians and their different generalizations.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/5312