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 SUqβ(3)β‘Uqβ(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.Comment: 5th International Conference on New Frontiers in Physics, Crete,
Greece, July 6-14, 201