科研之友
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摘要
Let A and B be unital algebras over a commutative ring R, and M be a (A, B)-bimodule, which is faithful as a left A-module and also as a right B-module. Let U = Tri(A, M, B) be the triangular algebra and V any algebra over R. Assume that Phi : U -> V is a Lie multiplicative isomorphism, that is, Phi satisfies Phi(ST - TS) = Phi (S)Phi(T) - Phi(T)Phi(S) for all S, T is an element of U. Then Phi(S + T) = Phi (S) + Phi(T) + Z(S,T) for all S, T is an element of U, where Z(S,T) is an element in the centre Z(V) of V depending on S and T.
