Abstract
Let be a triangular algebra over a commutative ring and be the centre of . Suppose that is an -bilinear mapping and that is a trace of . We describe the form of satisfying the condition for all . The question of when has the standard form will be addressed. Using the aforementioned trace function, we establish sufficient conditions for each Lie triple isomorphism on to be almost standard. As applications, we characterize Lie triple isomorphisms of upper triangular matrix algebras and nest algebras. Some further research topics related to current work are proposed at the end of this article.
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