  Algebraic deformations provide a systematic approach to generalizing the
symmetries of a physical theory through the introduction of new fundamental
constants. The applications of deformations of Lie algebras and Hopf algebras
to both spacetime and internal symmetries are discussed. As a specific example
we demonstrate how deforming the classical flavor group $SU(3)$ to the quantum
group $SU_q(3)\equiv U_q(su(3))$ (a Hopf algebra) and taking into account
electromagnetic mass splitting within isospin multiplets leads to new and
exceptionally accurate baryon mass sum rules that agree perfectly with
experimental data.
