Related papers: Generalized Derivations on Modules

The van Est map is a map from Lie groupoid cohomology (with respect to a sheaf taking values in a representation) to Lie algebroid cohomology. We generalize the van Est map to allow for more general sheaves, namely to sheaves of sections…

In this paper, we determine the derivation algebra and automorphism group of the twisted N=2 superconformal algebra. Then we generalize the relative results to the generalized twisted N=2 superconformal algebra in the final section.

A cohomology theory, associated to a $n$-Lie algebra and a representation space of it, is introduced. It is observed that this cohomology theory is qualified to encode the generalized derivation extensions, and that it coincides, for $n=3$,…

Let $A$ be a Banach algebra, not necessarily unital, and let $B$ be a closed subalgebra of $A$. We establish a connection between the Banach cyclic cohomology group $ {\cal{HC}}^n(A)$ of $A$ and the Banach $B$-relative cyclic cohomology…

This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…

A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…

Let $R$ be a Lie conformal algebra. The purpose of this paper is to investigate the conformal derivation algebra $CDer(R)$, the conformal quasiderivation algebra $QDer(R)$ and the generalized conformal derivation algebra $GDer(R)$. The…

Quantum general relativity may be considered as generally covariant QFT on differentiable manifolds, without any a priori metric structure. The kinematically covariance group acts by general diffeomorphisms on the manifold and by…

Suppose a group $\Gamma$ acts on a scheme $X$ and a Lie superalgebra $\mathfrak{g}$. The corresponding equivariant map superalgebra is the Lie superalgebra of equivariant regular maps from $X$ to $\mathfrak{g}$. We classify the irreducible…

We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra ${\cal A}$. Such a derivation, introduced by Bresar in 1991, is given by a linear mapping $u: {\cal A} \rightarrow {\cal A}$…

In this paper, we introduce the concept of the m-generalized right group inverse. This serves as a natural extension of both the m-weak group inverse and the generalized group inverse. We characterize this new generalized inverse using the…

For a manifold M we define a structure on the group action of Diff(M) on the smooth functions on M which reduces to the usual differential geometry upon differentiation at zero along the one-parameter groups of Diff(M). This ``integrated…

This paper primarily deals with the study of G-derivations associated with Lie-Yamaguti algebras. Taking G as an automorphism group, the concept of G-derivations, which is a derivation under both the bilinear and trilinear operations is…

We introduce a notion of generalized homogeneous derivations on graded rings as a natural extension of the homogeneous derivations defined by Kanunnikov. We then define gr-generalized derivations, which preserve the degrees of homogeneous…

Graded-division algebras are building blocks in the theory of finite-dimensional associative algebras graded by a group G. If G is abelian, they can be described, using a loop construction, in terms of central simple graded-division…

Let $\cA$ be a commutative unital Banach algebra, $\g$ be a semisimple complex Lie algebra and $G(\cA)$ be the 1-connected Banach--Lie group with Lie algebra $\g \otimes \cA$. Then there is a natural concept of a parabolic subgroup $P(\cA)$…

In this paper we first consider the Hamiltonian action of a compact connected Lie group on an $H$-twisted generalized complex manifold $M$. Given such an action, we define generalized equivariant cohomology and generalized equivariant…

In the main part of this paper a connection is just a fiber projection onto a (not necessarily integrable) distribution or sub vector bundle of the tangent bundle. Here curvature is computed via the Froelicher-Nijenhuis bracket, and it is…

We identify concrete examples of hypercyclic generalised derivations acting on separable ideals of operators and establish some necessary conditions for their hypercyclicity. We also consider the dynamics of elementary operators acting on…

The generalized Hyers--Ulam--Rassias stability of generalized derivations on unital Banach algebras into Banach bimodules is established.