  The notion of compatible braidings was introduced by Isaev, Ogievetsky and
Pyatov. On the base of this notion they defined certain quantum matrix algebras
generalizing the RTT algebras and Reflection Equation ones. They also defined
analogs of some symmetric polynomials in these algebras and showed that these
polynomials generate commutative subalgebras, called Bethe. By using a similar
approach we introduce certain new algebras called generalized Yangians and
define analogs of some symmetric polynomials in these algebras. We claim that
they commute with each other and thus generate a commutative Bethe subalgebra
in each generalized Yangian. Besides, we define some analogs (also arising from
couples of compatible braidings) of the Knizhnik-Zamolodchikov
equation--classical and quantum.
