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Annales Mathematicae Silesianae

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Lie Derivations on Trivial Extension Algebras

Amir Hosein Mokhtari
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  • Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran
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/ Fahimeh Moafian / Hamid Reza Ebrahimi Vishki
  • Department of Pure Mathematics, and Center of Excellence in Analysis., on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran
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Published Online: 2017-09-13 | DOI: https://doi.org/10.1515/amsil-2016-0017


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.

Keywords: derivation; Lie derivation; trivial extension algebra; triangular algebra


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About the article

Received: 2016-04-24

Accepted: 2016-09-16

Published Online: 2017-09-13

Published in Print: 2017-09-26

Citation Information: Annales Mathematicae Silesianae, Volume 31, Issue 1, Pages 141–153, ISSN (Online) 0860-2107, DOI: https://doi.org/10.1515/amsil-2016-0017.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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