If you want, I can produce a for a few pages/chapters of Sternberg to demonstrate how the mapping would work — or sketch a minimal working HTML/JavaScript prototype for the “Group Property Explorer”.
Sternberg’s rigorous treatment of group extensions, central extensions, and projective representations is directly applicable to understanding fractional quantum Hall states and topological insulators. His chapter on the representation theory of the Poincaré group (Wigner’s classification of particles by mass and spin) is the foundation of every quantum field theory course. group theory and physics sternberg pdf
I can tailor the explanation to your .
Week 5 — Roots, weights, and SU(n)