N = 4 $\mathcal{N}=4$ supersymmetric Yang-Mills theories with algebra so ( ) $\mathfrak {so}(4N)$ and appropriate choices of global structure can have non-invertible symmetries. We identify the branes holographically dual to symmetries, derive fusion rules for symmetries from worldvolume dynamics on branes.

Group-theoretic methods based on local symmetries are useful to construct invariant solutions of PDEs and to linearize nonlinear PDEs by invertible mappings. Local symmetries include point symmetries, contact symmetries and, more generally, Lie-Biicklund symmetries. An obvious limitation in their utility for particular PDEs is the non-existence of local symmetries. A given system of PDEs with a...