Abstract:
I'll introduce some new quantum algebras which are called Generalized Yangians. Their definition is based on the notion of compatible $R$-matrices. In these algebras quantum analogs of some symmetric polynomials (elementary ones, power sums) are well-defined. These quantum symmetric polynomials generate commutative subalgebras called Bethe. Also, I plan to exhibit some quantum analogs of the classical identities (Cayley-Hamilton, Newton) and discuss a version of the Drinfeld-Sokolov reduction in quantum algebras.
