  Polynomial Lie (super)algebras $g_{pd}$ are introduced via $G_{i}$-invariant
polynomial Jordan maps in quantum composite models with Hamiltonians $H$ having
invariance groups $G_{i}$. Algebras $g_{pd}$ have polynomial structure
functions in commutation relations, are related to pseudogroup structures $\exp
V, V\in g_{pd}$ and describe dynamic symmetry of models under study. Physical
applications of algebras $g_{pd}$ in quantum optics and in composite field
theories are briefly discussed.
