Related papers: Biderivations and commuting linear maps on Lie alg…

Let $\mathcal{L}$ be a subspace lattice on a Banach space $X$ and let $\delta:\mathrm{Alg}\mathcal{L}\rightarrow B(X)$ be a linear mapping. If $\vee\{L\in \mathcal{L}: L_-\nsupseteq L\}=X$ or $\wedge\{L_-:L\in \mathcal{L}, L_-\nsupseteq…

An algebra $L$ over a field $\Bbb F$, in which product is denoted by $[\,,\,]$, is said to be \textit{ Lie type algebra} if for all elements $a,b,c\in L$ there exist $\alpha, \beta\in \Bbb F$ such that $\alpha\neq 0$ and $[[a,b],c]=\alpha…

In this paper, we generalize the results about generalized derivations of Lie algebras to the case of BiHom-Lie algebras. In particular we give the classification of generalized derivations of Heisenberg BiHom-Lie algebras. The definition…

Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…

We introduce and study weak-2-local symmetric maps between C$^*$-algebras $A$ and $B$ as non necessarily linear nor continuous maps $\Delta: A\to B$ such that for each $a,b\in A$ and $\phi\in B^{*}$, there exists a symmetric linear map…

In this paper, we introduce the notion Lie-derivation. This concept generalizes derivations for non-Lie Leibniz algebras. We study these Lie-derivations in the case where their image is contained in the Lie-center, call them Lie-central…

Let $M$ be a prime $\Gamma$-ring satisfying a certain assumption and $D$ a nonzero derivation on $M$. Let $f:M\rightarrow M$ be a generalized derivation such that $f$ is centralizing and commuting on a left ideal $J$ of $M$. Then we prove…

In this paper, we prove that the variety $C_m(L)$ of commuting $m$-tuples of elements of simple Lie algebra $L$ is often reducible. Explicitely, we prove it is reducible for all simple Lie algebra $L$ not isomorphic to $\mathfrak{sl}_2$ and…

We prove that $L(X,Y)$ is complemented in $Lip_0(X, Y)$ (via a norm-one projection) provided that $Y$ is a dual space. Next, we introduce a vector-valued Lipschitz-free space $F_Y(X)$, a linear contraction $\beta_X^Y: F_Y(X) \to Y$ and…

In this paper, we study the connectedness of the commuting graph of a general Lie algebra and provide a process to determine whether the commuting graph is connected or not, as well as to compute an upper bound for its diameter. In…

In this paper, we characterize the biderivations of W-algebra $W(2,2)$ and Virasoro algebra $Vir$ without skewsymmetric condition. We get two classes of non-inner biderivations. As applications, we also get the forms of linear commuting…

Fix $a,b\in\C$, let $LW(a,b)$ be the loop $W(a,b)$ Lie algebra over $\C$ with basis $\{L_{\a,i},I_{\b,j} \mid \a,\b,i,j\in\Z\}$ and relations $[L_{\a,i},L_{\b,j}]=(\a-\b)L_{\a+\b,i+j},…

For any dg algebra $A$, not necessarily commutative, and a subset $S$ in $H(A)$, the homology of $A$, we construct its derived localisation $L_S(A)$ together with a map $A\to L_S(A)$, well-defined in the homotopy category of dg algebras,…

We construct a bialgebra object in the category of linear maps LM from a cocommutative rack bialgebra. The construction does extend to some non-cocommutative rack bialgebras, as is illustrated by a concrete example. As a separate result, we…

Let $\Gamma=(\mathcal{V},\mathcal{E})$ be a graph, whose vertices $v\in \mathcal{V}$ are colored black and white and labeled with invertible elements $\lambda_v$ from a commutative and associative ring $R$ containing $\pm 1$. Then we…

We consider the $\delta$-derivations of classical Lie superalgebras and prove that these superalgebras admit nonzero $\delta$-derivations only when $\delta = 0,1/2,1$. The structure of $1/2$-derivations for classical Lie superalgebras is…

Assume that B(X) is the algebra of all bounded linear operators on a complex Banach space X, and let W in B(X) is such that cl(W(X)) is not equal to X or W=zI, where z is a complex number and I is the identity operator. We show that if f:…

We prove new results on generalized derivations on C$^*$-algebras. By considering the triple product $\{a,b,c\} =2^{-1} (a b^* c + c b^* a)$, we introduce the study of linear maps which are triple derivations or triple homomorphisms at a…

A proof using the theory of completely positive maps is given to the fact that if $A \in M_2$, or $A \in M_3$ has a reducing eigenvalue, then every bounded linear operator $B$ with $W(B) \subseteq W(A)$ has a dilation of the form $I \otimes…

The construction of the Leavitt path algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. The new algebras, $L_K(E,C)$, are…