Abstract
Let be an arbitrary field with characteristic zero, let Tn
be the Lie algebra of all n × n upper triangular matrices over
with the Lie product [A,B] = A B − B A, and let a bijective map φ : Tn
→ Tn
satisfy φ ([A,B]) = [φ (A) , φ (B)], A,B ∊ Tn
. Then there exist an invertible matrix T ∊ Tn
, a function
satisfying ϕ (C) =0 for every strictly upper triangular matrix C ∊ Tn
, and an automorphism f of the field
, such that
for all [aij
]∊ Tn
, or
for all [aij
] ∊ Tn
, where
.
Acknowledgement
The author was supported in part by a grant from the Ministry of Higher Education, Science and Technology of Slovenia.