Polynomial lie algebras and associated pseudogroup structures in composite quantum models

Polynomial Lie (super)algebras ℷpd are introduced via Gi-invariant polynomial Jordan maps in quantum composite models with Hamiltonians H having invariance groups Gi. The algebras ℷpd have polynomial structure functions in commutation relations, they are related to pseudogroup structures by exp V, V ϵ ℷpd, and describe dynamical symmetry of models under study. Physical applications of algebras ℷpd in quantum optics and in composite field theories are briefly discussed.