Nonlinear \(\)-Jordan-type derivations on alternative \(\)-algebras

Let \(A\) be an unital alternative \(*\)-algebra. Assume that \(A\) contains a nontrivial symmetric idempotent element \(e\) which satisfies \(xA \cdot e = 0\) implies \(x = 0\) and \(xA \cdot (1_A - e) = 0\) implies \(x = 0\). In this paper, it is shown that \(\Phi\) is a nonlinear \(*\)-Jordan-typ...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Aline Jaqueline de Oliveira Andrade, Moraes, Gabriela C, Ruth Nascimento Ferreira, Macedo Ferreira, Bruno Leonardo
Format: Article
Language:English
Subjects:
Algebra
Derivation
Online Access:Get full text
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Summary:Let \(A\) be an unital alternative \(*\)-algebra. Assume that \(A\) contains a nontrivial symmetric idempotent element \(e\) which satisfies \(xA \cdot e = 0\) implies \(x = 0\) and \(xA \cdot (1_A - e) = 0\) implies \(x = 0\). In this paper, it is shown that \(\Phi\) is a nonlinear \(*\)-Jordan-type derivation on A if and only if \(\Phi\) is an additive \(*\)-derivation. As application, we get a result on alternative \(W^{*}\)-algebras.
ISSN:2331-8422
DOI:10.48550/arxiv.2105.00955