A NOTE ON LIE PRODUCT PRESERVING MAPS ON M-n(R)

作者：Marovt Janko^*

来源：Mathematica Slovaca, 2016, 66(3): 715-720.

DOI：10.1515/ms-2015-0173

• Lie product
• non-linear preserver
• commutativity

Let phi be an injective, continuous, Lie product preserving map on M-n(R), n > 3. In the paper we show that then there exist an invertible matrix T is an element of M-n(R) and a continuous function psi: M-n(R) -> R, where psi(A) = 0 for all matrices of trace zero, such that either phi(A) = TAT(-1) + psi(A)I for all A is an element of M-n(R), or phi(A) = -TA(t)T(-1) + psi(A)I for all A is an element of M-n(R).

• 出版日期2016-6