View source for 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

#Symmetry and [[../TrivialGroupoid/|groups]] #Galois groups and Galois theory
#Symmetry and [[../GroupoidHomomorphism2/|groupoids]]: internal and external symmetry
#Galois groupoids
#[[../QuantumFundamentalGroupoid/|fundamental groupoid functor]] #Extensions of Galois theory
#Tanaka-Krein duality
#Grothendieck extension of Tanaka-Krein duality to [[../AbelianCategory3/|non-Abelian]] groups
#Fourier duality
#[[../QuantumGroup4/|quantum groups]]
#Bravais lattices and their [[../TopologicalOrder2/|symmetry groups]]
#[[../GroupRepresentations/|group representations]] #[[../Matrix/|matrices]] and symmetry
#[[../TrivialGroupoid/|classification]] of groups and algebras
#`Broken symmetries' in [[../PhysicalMathematics2/|mathematical physics]] #Classical symmetries
#[[../HilbertBundle/|quantum symmetry]] and quantum groups
#Extended symmetry and [[../WeakHopfAlgebra/|quantum groupoids]]
#[[../DifferentialEquations/|differential equations]] and symmetry
#Symmetry and duality
#Groups and their dual algebras
#Symmetry, logic and categorical logics
#Symmetry resources: books, web links, conference announcement links, images, and so on
#The [[../CoIntersections/|algebraic]] dual of the non-Abelian [[../QuarkAntiquarkPair/|isospin]] group <math>SU(2)</math>
#SM theory groups, <math>U(1), SU(2), SU(3),...</math>
#[[../ECartan/|spinors]] and symmetry
#Symmetry in [[../LQG2/|quantum gravity]] and [[../SR/|general relativity]]

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