Lie triple derivations of triangular algebras
نویسندگان
چکیده
منابع مشابه
the structure of lie derivations on c*-algebras
نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولLie $^*$-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 کاملCharacterizing Lie derivations on triangular algebras by local actions
Let U = Tri(A,M,B) be a triangular algebra, where A, B are unital algebras over a field F and M is a faithful (A,B)-bimodule. Assume that ξ ∈ F and L : U → U is a map. It is shown that, under some mild conditions, L is linear and satisfies L([X, Y ]) = [L(X), Y ] + [X,L(Y )] for any X,Y ∈ U with [X, Y ] = XY − Y X = 0 if and only if L(X) = φ(X) + ZX + f(X) for all A, where φ is a linear derivat...
متن کاملAlternating triple systems with simple Lie algebras of derivations
We prove a formula for the multiplicity of the irreducible representation V (n) of sl(2, C) as a direct summand of its own exterior cube ΛV (n). From this we determine that V (n) occurs exactly once as a summand of ΛV (n) if and only if n = 3, 5, 6, 7, 8, 10. These representations admit a unique sl(2)-invariant alternating ternary structure obtained from the projection ΛV (n) → V (n). We calcul...
متن کاملDouble derivations of n-Lie algebras
After introducing double derivations of $n$-Lie algebra $L$ we describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual derivation Lie algebra $mathcal Der(L)$. In particular, we prove that the inner derivation algebra $ad(L)$ is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra wit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2012.04.015