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Commentary to: Generalized derivations of Lie triple systems

100%
Kaygorodov I., Popov Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
543-544
2
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Generalized derivations of Lie triple systems

100%
Zhou J., Chen L., Ma Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
260-271
EN
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.
3
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Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields

76%
Sun L., Liu W.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1332-1343
EN
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. This is achieved by studying the Hom-Lie superalgebra structures only on their 0-th and (−1)-th ℤ-components.
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