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Nonlinear Lie-type derivations of von Neumann algebras and related topics

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Fošner A., Wei F., Xiao Z.

Colloquium Mathematicum

2013

tom 132

nr 1

53-71

Motivated by the powerful and elegant works of Miers (1971, 1973, 1978) we mainly study nonlinear Lie-type derivations of von Neumann algebras. Let 𝓐 be a von Neumann algebra without abelian central summands of type I₁. It is shown that every nonlinear Lie n-derivation of 𝓐 has the standard form, that is, can be expressed as a sum of an additive derivation and a central-valued mapping which annihilates each (n-1)th commutator of 𝓐. Several potential research topics related to our work are also presented.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Fošner A.

1 Wei F.

1 Xiao Z.

1 2013

Wyniki wyszukiwania

Nonlinear Lie-type derivations of von Neumann algebras and related topics