On a new class of the commutative subalgebras of the maximal Gel'fand-Kirillov dimension in the universal enveloping algebra of a simple Lie algebra

New commutative subalgebras of the maximal Gel’fand-Kirillov dimension in the universal enveloping algebras of classical Lie algebras gl(n) and so(n) are constructed. In the case of sp(n) Gel’fand-Tsetlin algebra is extended to a maximally commutative one.