2014/11/22 by Ajda Fošner, Xinfeng Liang, Fosner, Ajda +5
Mathematics · #15A78 #15A86 #16W10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1411.6122
openalex publication_date 2014/11/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Let G be a generalized matrix algebra over a commutative ring R and Z(G) be the center of G. Suppose that \mathfrak q\colon G× G\longrightarrow G is an R-bilinear mapping and \mathfrak T\mathfrak q\colon G\longrightarrow G is the trace of \mathfrakq. We describe the form of \mathfrak T\mathfrak q satisfying the condition [\mathfrak T\mathfrak q(G), G]∈ Z(G) for all G∈ G. The question of when \mathfrak T\mathfrak q has the proper form is considered. Using the aforementioned trace function, we establish sufficient conditions for each Lie triple isomorphism of G 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.