Lie derivations on trivial extension algebras
Abstract
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
References
2. Benkovič D., Lie triple derivations of unital algebras with idempotents, Linear Multilinear Algebra 65 (2015), 141–165.
3. Cheung W.-S., Mappings on triangular algebras, PhD Dissertation, University of Victoria, 2000.
4. Cheung W.-S., Lie derivations of triangular algebras, Linear Multilinear Algebra 51 (2003), 299–310.
5. Du Y., Wang Y., Lie derivations of generalized matrix algebras, Linear Algebra Appl. 437 (2012), 2719–2726.
6. Ebrahimi Vishki H.R., Mirzavaziri M., Moafian F., Jordan higher derivations on trivial extension algebras, Commun. Korean Math. Soc. 31 (2016), 247–259.
7. Erfanian Attar A., Ebrahimi Vishki H.R., Jordan derivations on trivial extension algebras, J. Adv. Res. Pure Math. 6 (2014), 24–32.
8. Ghahramani H., Jordan derivations on trivial extensions, Bull. Iranian Math. Soc. 39 (2013), 635–645.
9. Ji P., Qi W., Charactrizations of Lie derivations of triangular algebras, Linear Algebra Appl. 435 (2011), 1137–1146.
10. Martindale III W.S., Lie derivations of primitive rings, Michigan Math. J. 11 (1964), 183–187.
11. Moafian F., Higher derivations on trivial extension algebras and triangular algebras, PhD Thesis, Ferdowsi University of Mashhad, 2015.
12. Moafian F., Ebrahimi Vishki H.R., Lie higher derivations on triangular algebras revisited, Filomat 30 (2016), no. 12, 3187–3194.
13. Mokhtari A.H., Ebrahimi Vishki H.R., More on Lie derivations of generalized matrix algebras, Preprint 2015, arXiv: 1505.02344v1.
14. Wang Y., Lie n-derivations of unital algebras with idempotents, Linear Algebra Appl. 458 (2014), 512–525.
15. Zhang Y., Weak amenability of module extensions of Banach algebras, Trans. Amer. Math. Soc. 354 (2002), 4131–4151.
Department of Pure Mathematics, Ferdowsi University of Mashhad, Iran Iran, Islamic Republic of
Department of Pure Mathematics, Ferdowsi University of Mashhad, Iran Iran, Islamic Republic of
Department of Pure Mathematics & Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Iran Iran, Islamic Republic of
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