
Higher ξLie derivable maps on triangular algebras at reciprocal elements
 ZHANG Xia, ZHANG Jianhua

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(10):
7984.
doi:10.6040/j.issn.16719352.0.2019.192

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Let U=Tri(A,M,B )be a triangular algebra with identity 1, 1_{A},1_{B} be the unit of A and B, respectively. For any A∈A, B∈B, there are integers k_{}1,k_{}2 respectively, making k_{1}1_{A}A, k_{2}1_{B}B invertible in triangular algebras. {φ_{n}}_{n}∈N:U→U be a sequence of linear maps. In this paper, we prove that if {φ_{n}}_{n}∈N satisfies φ_{n}(［U,V］_{ξ})=∑_{i+j=n}φ_{i}(U)φ_{j}(V)ξφ_{i}(V)φ_{j}(U)(ξ≠0,1), for any U,V∈U with UV=VU=1, then {φ_{n}}_{n}∈N is a higher derivation, where φ_{}0=id_{}0 is the identity map, ［U,V］_{ξ}=UVξVU.