G-invariant polynomial extensions of Lie algebras in quantum many-body physics

A new class of Lie-algebraic structures g d is revealed in some multi-particle processes of quantum physics having internal symmetry groups G inv . They are extensions of some Lie algebras h (via coset construction) by G-invariant h-tensors v which are polynomials in boson operators. Applications of these algebras are briefly discussed for solving spectral and evolution tasks with g d as their dynamic symmetry algebras.