Abstract
Let be a generalized matrix algebra over a commutative ring and be the centre of . Suppose that is an -bilinear mapping and is the trace of . We describe the form of satisfying the condition for all . The question of when has the proper form is considered. Using the aforementioned trace function, we establish sufficient conditions for each Lie triple isomorphism of to be almost standard. As applications we characterize Lie triple isomorphisms of full matrix algebras, of triangular algebras and of certain unital algebras with nontrivial idempotents. Some topics for future research closely related to our current work are proposed at the end of this article.
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