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Jordan superderivations and Jordan triple superderivations of superalgebras

100%
Yuan H., Chen L.
Colloquium Mathematicum
|
2016
|
tom 144
|
nr 2
229-243
EN
We study Jordan (θ,θ)-superderivations and Jordan triple (θ,θ)-superderivations of superalgebras, using the theory of functional identities in superalgebras. As a consequence, we prove that if A = A₀ ⊕ A₁ is a prime superalgebra with deg(A₁) ≥ 9, then Jordan superderivations and Jordan triple superderivations of A are superderivations of A, and generalized Jordan superderivations and generalized Jordan triple superderivations of A are generalized superderivations of A.
2
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The classification of modular Lie superalgebras of type M

100%
Ma L., Chen L.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
The natural filtration of the infinite-dimensional simple modular Lie superalgebra M over a field of characteristic p > 2 is proved to be invariant under automorphisms by discussing ad-nilpotent elements. Moreover, an intrinsic property is obtained and all the infinite-dimensional simple modular Lie superalgebras M are classified up to isomorphisms. As an application, a property of automorphisms of M is given.
3
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Restricted and quasi-toral restricted Lie-Rinehart algebras

100%
Sun B., Chen L.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension should be.
4
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Generalized derivations of Lie triple systems

81%
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.
5
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Uniqueness of decomposition of pseudo-Riemannian superalgebras

81%
Zheng K., Chen L., Zhang Y.
Colloquium Mathematicum
|
2014
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tom 136
|
nr 1
109-123
EN
This paper is primarily concerned with pseudo-Riemannian superalgebras, which are superalgebras endowed with pseudo-Riemannian non-degenerate supersymmetric consistent bilinear forms. Decompositions of pseudo-Riemannian superalgebras whose left centers are isotropic and whose left centers are not isotropic are investigated.
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