Multiplicative Lie skew derivations on triangular algebras

Abstract

Let U be a triangular algebra. Under certain assumptions, we show that every multiplicative Lie σ -derivation L : U → U is of the form δ + τ, where δ is an additive σ -derivation on U and τ is a map from U to its center Z σ ( U ) that vanishes on Lie product. As an application, we study the multiplicative Lie σ -derivation on nest algebras and block upper triangular matrix algebras.