Adjacency preserving maps on upper triangular matrix algebras Original Research Article

Let n be an integer, ngreater-or-equal, slanted3, and Tn the algebra of all real n×n upper triangular matrices. We describe the general form of maps on Tn that preserve the adjacency in both directions. We apply this result to characterize the semigroup of injective continuous maps on Tn preserving the adjacency in one direction only.