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Generalized derivations of Lie triple systems

Jia Zhou, Liangyun Chen, Yao Ma (2016)

Open Mathematics

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.

Homogeneous Einstein manifolds based on symplectic triple systems

Cristina Draper Fontanals (2020)

Communications in Mathematics

For each simple symplectic triple system over the real numbers, the standard enveloping Lie algebra and the algebra of inner derivations of the triple provide a reductive pair related to a semi-Riemannian homogeneous manifold. It is proved that this is an Einstein manifold.

On generalized Jordan derivations of Lie triple systems

Abbas Najati (2010)

Czechoslovak Mathematical Journal

Under some conditions we prove that every generalized Jordan triple derivation on a Lie triple system is a generalized derivation. Specially, we conclude that every Jordan triple θ -derivation on a Lie triple system is a θ -derivation.

Restricted and quasi-toral restricted Lie-Rinehart algebras

Bing Sun, Liangyun Chen (2015)

Open Mathematics

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....

Simple multilinear algebras and hermitian operators

T. S. R. Fuad, Jon D. Phillips, Xiaorong Shen, Jonathan D. H. Smith (2000)

Commentationes Mathematicae Universitatis Carolinae

The paper studies multilinear algebras, known as comtrans algebras, that are determined by so-called T -Hermitian matrices over an arbitrary field. The main result of this paper shows that the comtrans algebra of n -dimensional T -Hermitian matrices furnishes a simple comtrans algebra.

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