Displaying similar documents to “Commentary to: Generalized derivations of Lie triple systems”

Generalized derivations of Lie triple systems

Jia Zhou, Liangyun Chen, Yao Ma (2016)

Open Mathematics

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In this paper, we present some basic properties concerning the derivation algebra Der (T), the quasiderivation algebra QDer (T) and the generalized derivation algebra GDer (T) of a Lie triple system T, with the relationship Der (T) ⊆ QDer (T) ⊆ GDer (T) ⊆ End (T). Furthermore, we completely determine those Lie triple systems T with condition QDer (T) = End (T). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.

Lie Derivations on Trivial Extension Algebras

Amir Hosein Mokhtari, Fahimeh Moafian, Hamid Reza Ebrahimi Vishki (2017)

Annales Mathematicae Silesianae

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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.

Stability of commuting maps and Lie maps

J. Alaminos, J. Extremera, Š. Špenko, A. R. Villena (2012)

Studia Mathematica

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Let A be an ultraprime Banach algebra. We prove that each approximately commuting continuous linear (or quadratic) map on A is near an actual commuting continuous linear (resp. quadratic) map on A. Furthermore, we use this analysis to study how close are approximate Lie isomorphisms and approximate Lie derivations to actual Lie isomorphisms and Lie derivations, respectively.

Vector form brackets in Lie algebroids

Albert Nijenhuis (1996)

Archivum Mathematicum

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A brief exposition of Lie algebroids, followed by a discussion of vector forms and their brackets in this context - and a formula for these brackets in “deformed” Lie algebroids.

Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields

Liping Sun, Wende Liu (2017)

Open Mathematics

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According to the classification by Kac, there are eight Cartan series and five exceptional Lie superalgebras in infinite-dimensional simple linearly compact Lie superalgebras of vector fields. In this paper, the Hom-Lie superalgebra structures on the five exceptional Lie superalgebras of vector fields are studied. By making use of the ℤ-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie superalgebra structures on exceptional simple Lie superalgebras....