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Lie Maps on Triangular Algebras Without Assuming Unity

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Abstract

We characterize Lie centralizer, Lie derivations and generalized Lie 2-derivations at zero products on triangular algebras without assuming unity. Further more, the Lie centralizers, Lie derivations and generalized Lie 2-derivations will be described for triangular algebras. Also, several examples are presented which illustrate limitations on extending some of the theory developed. The obtained results will be used for upper triangular matrix algebras (not necessarily unital) and nest algebras. Our results will also generalize some of the previous results.

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Acknowledgements

The authors like to express their sincere thanks to the referee(s) of this paper.

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  1. Department of Mathematics Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Iran

    Roonak Behfar & Hoger Ghahramani

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  1. Roonak Behfar
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  2. Hoger Ghahramani
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Correspondence to Hoger Ghahramani.

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Behfar, R., Ghahramani, H. Lie Maps on Triangular Algebras Without Assuming Unity. Mediterr. J. Math. 18, 215 (2021). https://doi.org/10.1007/s00009-021-01836-z

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  • DOI: https://doi.org/10.1007/s00009-021-01836-z

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