Generalized Derivations of Lie Superalgebras
Generalized Derivations of Lie Superalgebras
复制标题
DOI：
10.1080/00927870903236228
复制
发表时间：
2010-09
影响因子：
0.7
通讯作者：
Runxuan Zhang;Yongzheng Zhang
中科院分区：
文献类型：
--
作者：
Runxuan Zhang;Yongzheng Zhang
设𝔽是特征≠2的域，ℒ是𝔽上的有限维李超代数。本文研究了ℒ的导子超代数Der(ℒ)、拟导子超代数QDer(ℒ)和广义导子超代数GDer(ℒ)，它们构成了一个塔式Der(ℒ)⊆QDer(ℒ)⊆)GDer(ℒ)⊆pl(ℒ))，其中pl(ℒ)表示一般的线性李超代数。更确切地说，我们完全刻画了那些李超代数ℒ的QDer(ℒ)=pl(ℒ)。我们证明了ℒ的拟导子可以作为导子嵌入到更大的李超代数中，并且当ℒ的零化子等于零时，我们得到了的半直和分解。
Let 𝔽 be a field of characteristic ≠ 2 and ℒ a finite-dimensional Lie superalgebra over 𝔽. In this article, we study the derivation superalgebra Der(ℒ), the quasiderivation superalgebra QDer(ℒ), and the generalized derivation superalgebra GDer(ℒ) of ℒ, which form a tower Der(ℒ) ⊆ QDer(ℒ) ⊆ GDer(ℒ) ⊆ pl(ℒ), where pl(ℒ) denotes the general linear Lie superalgebra. More precisely, we characterize completely those Lie superalgebras ℒ for which QDer(ℒ) = pl(ℒ). We prove that the quasiderivations of ℒ can be embedded as derivations in a larger Lie superalgebra and, furthermore, when the annihilator of ℒ is equal to zero, we obtain a semidirect sum decomposition of .