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Commuting traces and commutativity preserving maps on triangular algebras. (English) Zbl 1076.16032

The main result of the paper gives sufficient conditions under which every commuting trace of a bilinear map on a triangular algebra is of a standard form. These conditions are too technical to be stated here; let us just mention that they are fulfilled in the most important examples of triangular algebras. The main result is applied to the study of Lie isomorphisms and commutativity preserving maps on triangular algebras, yielding generalizations of several known results concerning these maps on some special triangular algebras (algebras of upper triangular matrices, nest algebras).

MSC:

16W20 Automorphisms and endomorphisms
16R50 Other kinds of identities (generalized polynomial, rational, involution)
16W22 Actions of groups and semigroups; invariant theory (associative rings and algebras)
16S50 Endomorphism rings; matrix rings
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