Automorphisms, σ-Biderivations and σ-Commuting Maps of Triangular Algebras

Let σ be an automorphism of an arbitrary algebra. In this paper, we introduce the notions of inner and extremal σ -biderivations and of proper σ -commuting maps. We prove that (under certain assumptions) every σ -biderivation of a triangular algebra is the sum of an extremal σ -biderivation and an inner σ -biderivation; and provide sufficient conditions on a triangular algebra for all of its σ -biderivations (respectively, σ -commuting maps) to be inner (respectively, proper). We introduce and describe a new class of automorphisms of triangular algebras. We provide many classes of triangular algebras whose automorphisms can be determined.