A generalization on derivations of Lie algebras
نویسندگان
چکیده
<p style='text-indent:20px;'>We initiate a study on range of new generalized derivations finite-dimensional Lie algebras over an algebraically closed field characteristic zero. This generalization has analogue in the theory associative prime rings and unites many well-known that have already appeared extensively other nonassociative algebras. After exploiting fundamental properties, we introduce analyze their interiors, especially focusing rationality corresponding Hilbert series. Applying techniques computational ideal develop approach to explicitly compute these for three-dimensional special linear algebra complex field.</p>
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 کاملLie-type higher derivations on operator algebras
Motivated by the intensive and powerful works concerning additive mappings of operator algebras, we mainly study Lie-type higher derivations on operator algebras in the current work. It is shown that every Lie (triple-)higher derivation on some classical operator algebras is of standard form. The definition of Lie $n$-higher derivations on operator algebras and related pot...
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 کاملCharacterization of Lie higher Derivations on $C^{*}$-algebras
Let $mathcal{A}$ be a $C^*$-algebra and $Z(mathcal{A})$ the center of $mathcal{A}$. A sequence ${L_{n}}_{n=0}^{infty}$ of linear mappings on $mathcal{A}$ with $L_{0}=I$, where $I$ is the identity mapping on $mathcal{A}$, is called a Lie higher derivation if $L_{n}[x,y]=sum_{i+j=n} [L_{i}x,L_{j}y]$ for all $x,y in mathcal{A}$ and all $ngeqslant0$. We show that ${L_{n}}_{n...
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: Electronic research archive
سال: 2021
ISSN: ['2688-1594']
DOI: https://doi.org/10.3934/era.2020124