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 [[../TrivialGroupoid/|groups]] #Galois groups and Galois theory
2. Symmetry and [[../GroupoidHomomorphism2/|groupoids]]: internal and external symmetry
3. Galois groupoids
4. [[../QuantumFundamentalGroupoid/|fundamental groupoid functor]] #Extensions of Galois theory
5. Tanaka-Krein duality
6. Grothendieck extension of Tanaka-Krein duality to [[../AbelianCategory3/|non-Abelian]] groups
7. Fourier duality
8. [[../QuantumGroup4/|quantum groups]]
9. Bravais lattices and their [[../TopologicalOrder2/|symmetry groups]]
10. [[../GroupRepresentations/|group representations]] #[[../Matrix/|matrices]] and symmetry
11. [[../TrivialGroupoid/|classification]] of groups and algebras
12. `Broken symmetries' in [[../PhysicalMathematics2/|mathematical physics]] #Classical symmetries
13. [[../HilbertBundle/|quantum symmetry]] and quantum groups
14. Extended symmetry and [[../WeakHopfAlgebra/|quantum groupoids]]
15. [[../DifferentialEquations/|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 [[../CoIntersections/|algebraic]] dual of the non-Abelian [[../QuarkAntiquarkPair/|isospin]] group $SU(2)$
21. SM theory groups, $U(1),SU(2),SU(3),...$
22. [[../ECartan/|spinors]] and symmetry
23. Symmetry in [[../LQG2/|quantum gravity]] and [[../SR/|general relativity]]