Symmetry in mathematics (Q1205893)

An attempt to give an exposition of the symmetry concept is presented starting from the determination of the symmetry groups for objects of various categories: finite sets, vector spaces and manifolds with differential and algebraic structures. The main ideas of Galois, Lie, Chevalley, Killing, Cartan, Weyl, Gelfand, Harish-Chandra, Langlands and others are listed in their connection with the corresponding physical applications. The latest investigations associated with gauge transformations and loop groups as well as with quantum groups and noncommutative geometry are also mentioned.