منابع مشابه
On Derivation Algebras of Malcev Algebras and Lie Triple Systems
W. H. Davenport has shown that the derivation algebra 3)(4) of a semisimple Malcev algebra A of characteristic 0 acts completely reducibly on A. The purpose of the present note is to characterize those Malcev algebras which have such derivation algebras as those whose radical is central and to obtain the same result for Lie triple systems. Analogous results are known to hold for standard and al...
متن کاملGeneralized Derivation Tower Theorem of Lie algebras
We give an algorithm of decomposition for a finite-dimensional Lie algebra over a field of characteristic 0 permitting to generalize the derivation tower theorem of Lie algebras.
متن کاملLie Algebras: Abstract Theory of Weights
Proof. I will check the four axioms of the root system. (R1) Since |Φ∨| = |Φ|, then Φ∨ is finite. Since Φ spans E and α∨ is a non-zero scalar multiple of α for all α ∈ Φ, then Φ∨ spans E and 0 / ∈ Φ∨. (R2) Since (−α)∨ = 2(−α) ((−α),(−α)) = − 2α (α,α) = −α∨, then the only multiples of α∨ are ±α∨. (R3) I need to show that if α∨ ∈ Φ∨ then the reflection σα∨ leaves Φ∨ invariant. Let α in Φ, then fo...
متن کاملLie $^*$-double derivations on Lie $C^*$-algebras
A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...
متن کاملNote on The Generalized Derivation Tower Theorem for Lie algebras
We provide an algorithm for decomposing a finite-dimensional Lie algebra over a field of characteristic 0 permitting to generalize the derivation tower theorem for Lie algebras, is proved by E. Schenkman [4].
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1937
ISSN: 0002-9947
DOI: 10.2307/1989656