$\sigma$-Centralizers of triangular algebras

M.  Ashraf; M. A.  Ansari

doi:10.37863/umzh.v75i4.6924

M. Ashraf Department of Mathematics, Aligarh Muslim University, India
M. A. Ansari Department of Mathematics, Aligarh Muslim University, India

DOI: https://doi.org/10.37863/umzh.v75i4.6924

Keywords: Triangular algebra; $\sigma$-centralizer; Lie $\sigma$-centralizer; Jordan $\sigma$-centralizer.

Abstract

UDC 512.5

In this paper, we characterize Lie (Jordan) $\sigma$-centralizers of triangular algebras. More precisely, we prove that, under certain conditions, every Lie $\sigma$-centralizer of a triangular algebra can be represented as the sum of a $\sigma$-centralizer and a central-valued mapping. Further, it is shown that every Jordan $\sigma$-centralizer of a triangular algebra is a $\sigma$-centralizer.

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