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Generalized Lie $ n $-derivations on generalized matrix algebras
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<p>Let $ \mathcal{G} $ be a generalized matrix algebra. We show that under certain conditions, each generalized Lie $ n $-derivation associated with a linear map on $ \mathcal{G} $ is a sum of a generalized derivation and a central map vanishing on all $ (n-1) $-th commutators and is also a sum of a generalized inner derivation and a Lie $ n $-derivation. As an application, generalized Lie $ n $-derivations on von Neumann algebras are characterized.</p>
American Institute of Mathematical Sciences (AIMS)
Title: Generalized Lie $ n $-derivations on generalized matrix algebras
Description:
<p>Let $ \mathcal{G} $ be a generalized matrix algebra.
We show that under certain conditions, each generalized Lie $ n $-derivation associated with a linear map on $ \mathcal{G} $ is a sum of a generalized derivation and a central map vanishing on all $ (n-1) $-th commutators and is also a sum of a generalized inner derivation and a Lie $ n $-derivation.
As an application, generalized Lie $ n $-derivations on von Neumann algebras are characterized.
</p>.
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