PlanetPhysics/Topic on Groupoid Symmetries and Duality

Symmetry groups, groupoids, algebras and duality
This is a new topic by multiple contributors of substantial interest to both mathematicians and mathematical physicists or theoreticians. Any significant content additions are welcome. The following list is open to additions and expansion


 * 1) Symmetry and groups #Galois groups and Galois theory
 * 2) Symmetry and groupoids: internal and external symmetry
 * 3) Galois groupoids
 * 4) fundamental groupoid functor #Extensions of Galois theory
 * 5) Tanaka-Krein duality
 * 6) Grothendieck extension of Tanaka-Krein duality to non-Abelian groups
 * 7) Fourier duality
 * 8) quantum groups
 * 9) Bravais lattices and their symmetry groups
 * 10) group representations #matrices and symmetry
 * 11) classification of groups and algebras
 * 12) `Broken symmetries' in mathematical physics #Classical symmetries
 * 13) quantum symmetry and quantum groups
 * 14) Extended symmetry and quantum groupoids
 * 15) differential equations and symmetry
 * 16) Symmetry and duality
 * 17) Groups and their dual algebras
 * 18) Symmetry, logic and categorical logics
 * 19) Symmetry resources: books, web links, conference announcement links, images, and so on
 * 20) The algebraic dual of the non-Abelian isospin group $$SU(2)$$
 * 21) SM theory groups, $$U(1), SU(2), SU(3),...$$
 * 22) spinors and symmetry
 * 23) Symmetry in quantum gravity and general relativity