Related papers: On algebras generated by inner derivations

In this paper we generalize classical results on Lie algebras and universal enveloping algebras of Lie algebras to Lie-Rinehart algebras. We define for any Lie-Rinehart algebra $L$ and any cocycle $f$ in $Z^2(L,B)$, a universal enveloping…

In this paper we introduce (weakly) root graded Banach--Lie algebras and corresponding Lie groups as natural generalizations of group like $\GL_n(A)$ for a Banach algebra $A$ or groups like $C(X,K)$ of continuous maps of a compact space $X$…

We obtain a realization of the Lie superalgebra $D(2, 1 ; \alpha)$ in differential operators on the supercircle $S^{1|2}$ and in $4\times 4$ matrices over a Weyl algebra. A contraction of $D(2, 1 ; \alpha)$ is isomorphic to the universal…

We proof some basic tools about spaces of H"older-continuous functions between (in general infinite dimensional) Banach spaces and use them to construct new examples of infinite dimensional (LB)-Lie groups.

Given a pair of (real or complex) Lie algebroid structures on a vector bundle $A$ (over $M$) and its dual $A^*$, and a line bundle $\module$ such that $\module\otimes\module=(\wedge^{\TOP} A^*\otimes\wedge^{\TOP} T^*M)$, there exist two…

In this paper, we prove that every completely contractive dual Banach algebra is completely isometric to a $w^\ast$-closed subalgebra the operator space of completely bounded linear operators on some reflexive operator space.

We develop a general framework for the analysis of operator-valued multilinear multipliers acting on Banach-valued functions. Our main result is a Coifman-Meyer type theorem for operator-valued multilinear multipliers acting on suitable…

Given Banach spaces $\mathcal{X}$ and $\mathcal{Y}$ and Banach space operators $A\in L(\mathcal{X})$ and $B\in L(\mathcal{Y}).$ The generalized derivation $\delta_{A,B} \in L(L(\mathcal{Y},\mathcal{X}))$ is defined by…

We generalise Wigner's theorem to its most general form possible for B(h) in the sense of completely characterising those vector state transformations of B(h) that appear as restrictions of duals of linear operators on B(h). We then use…

Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three…

Given $L$ a complex solvable finite dimensional Lie Algebra of operators acting on a Banach space $E$ and $\{ x_i\}_{1\le i\le n}$ a Jordan-H\"older basis of $ L$, we study the relation between $Sp(L,E)$ and $\Pi Sp(x_i)$.

The closed subalgebra $\mathcal J$ of the Banach algebra $\mathcal L(X)$ of bounded linear operators on the Banach space $X$ is a non-trivial closed $\mathcal I$-subideal of $\mathcal L(X)$ if $\mathcal I$ is a closed ideal of $\mathcal…

We study classical R-matrices D for Lie algebras L such that D is also a derivation of L. This yields derivation double Lie algebras (L,D). The motivation comes from recent work on post-Lie algebra structures on pairs of Lie algebras…

In this paper, first we show that $(\g,[\cdot,\cdot],\alpha)$ is a hom-Lie algebra if and only if $(\Lambda \g^*,\alpha^*,d)$ is an $(\alpha^*,\alpha^*)$-differential graded commutative algebra. Then, we revisit representations of hom-Lie…

In this paper, we study {\it operator spaces\/} in the sense of the theory developed recently by Blecher-Paulsen [BP] and Effros-Ruan [ER1]. By an operator space, we mean a closed subspace $E\subset B(H)$, with $H$ Hilbert. We will be…

In this paper we study two types of collections of operators on a Banach space on the subject of forming operator ideals. One of the types allows us to construct an uncountable chain of closed ideals in each of the operator algebras…

We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p>2. A superalgebra generalization of the celebrated Kac-Weisfeiler Conjecture is formulated, which exhibits a…

Let $W_X(\mathbb{F})$ be the Lie algebra of all derivations of the polynomial algebra $\mathbb{F}[X]$ in infinitely many variables. We describe all derivations of $W_X(\mathbb{F})$ over a field of characteristic zero and prove that all such…

We generalise the Riesz representation theorems for positive linear functionals on $\mathrm{C}_{\mathrm c}(X)$ and $\mathrm{C}_{\mathrm 0}(X)$, where $X$ is a locally compact Hausdorff space, to positive linear operators from these spaces…

Given a complex Banach space $X$ and a joint spectrum for complex solvable finite dimensional Lie algebras of operators defined on $X$, we extend this joint spectrum to quasi-solvable Lie algebras of operators, and we prove the main…