ABSTRACT
Let UTm be the algebra of all m × m upper triangular matrices over a field whose characteristic is different from 2. Given an involution * of the first kind on UTm, we will obtain the minimal integer t such that the Lie polynomial [[z1, z2], …, [z2t−1, z2t]] is an identity for
. Afterwards, under a mild technical restriction on
, we will describe all multilinear Lie polynomials whose image evaluated on K(m, *) is the space formed by all strictly upper triangular matrices of K(m, *).
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