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Hometopic: groupoid symmetry and duality

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# topic: groupoid symmetry and duality

# 0.1 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. 2. 3. Symmetry and groupoids: internal and external symmetry

4. Galois groupoids

5. 6. Extensions of Galois theory

7. Tanaka-Krein duality

8. Grothendieck extension of Tanaka-Krein duality to non-Abelian groups

9. Fourier duality

10. 11. Bravais lattices and their symmetry groups

12. 13. Matrices and symmetry

14. Classification of groups and algebras

15. ‘Broken symmetries’ in mathematical physics

16. Classical symmetries

17. Quantum symmetry and quantum groups

18. Extended symmetry and quantum groupoids

19. Differential equations and symmetry

20. Symmetry and duality

21. Groups and their dual algebras

22. Symmetry, logic and categorical logics

23. 24. The algebraic dual of the non-Abelian isospin group $SU(2)$

25. SM theory groups, $U(1),SU(2),SU(3),...$

26. Spinors and symmetry

27. Symmetry in quantum gravity and general relativity

## Mathematics Subject Classification

18-00*no label found*22A22

*no label found*

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