Abstract
Let \(\sigma \) be an automorphism of an arbitrary algebra. In this paper, we introduce the notions of inner and extremal \(\sigma \)-biderivations and of proper \(\sigma \)-commuting maps. We prove that (under certain assumptions) every \(\sigma \)-biderivation of a triangular algebra is the sum of an extremal \(\sigma \)-biderivation and an inner \(\sigma \)-biderivation; and provide sufficient conditions on a triangular algebra for all of its \(\sigma \)-biderivations (respectively, \(\sigma \)-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.
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González, C.M., Repka, J. & Sánchez-Ortega, J. Automorphisms, \(\sigma \)-Biderivations and \(\sigma \)-Commuting Maps of Triangular Algebras. Mediterr. J. Math. 14, 68 (2017). https://doi.org/10.1007/s00009-016-0809-2
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DOI: https://doi.org/10.1007/s00009-016-0809-2