Lie Derivations on Trivial Extension Algebras

Lie Derivations on Trivial Extension Algebras

In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be expressed as a sum of a derivation and a center valued map vanishing at commutators. We then apply our results for triangular algebras. Some illuminating examples are al...

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Veröffentlicht in:Annales mathematicae Silesianae 2017-09, Vol.31 (1), p.141-153
Hauptverfasser: Mokhtari, Amir Hosein, Moafian, Fahimeh, Vishki, Hamid Reza Ebrahimi
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derivation
Lie derivation
triangular algebra
trivial extension algebra
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container_title Annales mathematicae Silesianae
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creator Mokhtari, Amir Hosein
Moafian, Fahimeh
Vishki, Hamid Reza Ebrahimi
description In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be expressed as a sum of a derivation and a center valued map vanishing at commutators. We then apply our results for triangular algebras. Some illuminating examples are also included.
doi_str_mv 10.1515/amsil-2016-0017
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subjects derivation
Lie derivation
triangular algebra
trivial extension algebra
title Lie Derivations on Trivial Extension Algebras
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