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Let N(F) be the Lie algebra consisting of all strictly upper triangular (n+ 1)× (n+ 1) matrices over a field F . A map φ on N(F) is called to be anti-commuting if [φ(x),y] = −[x,φ(y)] for any x,y ∈ N(F) . We show that for n 4 , a nonlinear map φ : N(F) → N(F) is anti-commuting if and only if there exist b,b1,b2 ∈ F and a nonlinear function f : N(F) → F such that φ = ad (bE2n)+ μ (n,n+1) b2 + μ b1 + φ f , where ad (bE2n) is an inner anti-commuting map, μ b2 ,μ (12) b1 are extremal anti-commuting maps, φ f is a central anti-commuting map. Mathematics subject classification (2010): 15A04, 15A27, 15A86.

Nonlinear anti-commuting maps of strictly triangular matrix Lie algebras