Related papers: Derivations on four dimensional genetic Volterra a…

This note intertwines the concepts of degeneration and contraction of algebras and quadratic forms defined on a vector space V . The general linear group GL(V ) acts regularly on the spaces of these two objects. The base field is taken to…

We introduce the notion of maximal orders over quaternion algebras with orthogonal involution and give a classification over local fields, and a partial classification over algebraic number fields.

In this paper we prove that any nonlinear Jordan derivation on triangular algebras is an additive derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert spaces is inner.

The paper is devoted to local derivations on the algebra $S(\mathcal{M},\tau)$ of $\tau$-measurable operators affiliated with a von Neumann algebra $\mathcal{M}$ and a faithful normal semi-finite trace $\tau.$ We prove that every local…

Let $A$ be an MV-algebra. An $(\odot,\vee)$-derivation on $A$ is a map $d: A\to A$ satisfying: $d(x \odot y) = (d(x) \odot y) \vee(x \odot d(y))$ for all $x, y \in A$. This paper initiates the study of $(\odot,\vee)$-derivations on…

We defined \delta-derivations of n-ary algebras. We described \delta-derivations of (n+1)-dimensional n-ary Filippov algebras and simple finite-dimensional Filippov algebras over algebraically closed field zero characteristic, and simple…

For all the convolution algebras $L^1[0,1),\ L^1_{\text{loc}}$ and $A(\omega)=\bigcap_n L^1(\omega_n)$, the derivations are of the form $D_{\mu} f=Xf*\mu$ for suitable measures $\mu$, where $(Xf)(t)=tf(t)$. We describe the (weakly) compact…

We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…

We describe derivations of the Clifford algebra of a nondegenerate quadratic form on a countable dimensional vector space over an algebraically closed field of characteristic not equal to $2$. We also construct an algebraic automorphism of…

Let $K$ be a field of characteristic zero and $\mathcal A$ a $K$-algebra such that all the $K$-subalgebras generated by finitely many elements of $\mathcal A$ are finite dimensional over $K$. A $K$-$\mathcal E$-derivation of $\mathcal A$ is…

We prove that every {\rm(}not necessarily linear nor continuous{\rm)} 2-local triple derivation on a von Neumann algebra $M$ is a triple derivation, equivalently, the set Der$_{t} (M)$, of all triple derivations on $M,$ is algebraically…

We study a family of dissections of flow polytopes arising from the subdivision algebra. To each dissection of a flow polytope, we associate a polynomial, called the left-degree polynomial, which we show is invariant of the dissection…

This paper initiates the study of 2-local derivations on Lie algebras over fields of prime characteristic. Let $\mathfrak{g}$ be a simple Jacobson-Witt algebra $W_n$ over a field of prime characteristic $p$ with cardinality no less than…

We study the covariant derivatives of an eigenfunction for the Laplace-Beltrami operator on a complete, connected Riemannian manifold with nonzero constant sectional curvature. We show that along every parallel tensor, the covariant…

Let $\theta$ be an isomorphism on $L_0^{\infty} (w)^*$. In this paper, we investigate $\theta$-generalized derivations on $L_0^{\infty} (w)^*$. We show that every $\theta$-centralizing $\theta$-generalized derivation on $L_0^{\infty} (w)^*$…

This is the fourth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…

In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.

In this paper, at first the construction of Lie higher derivations and higher derivations on a generalized matrix algebra were characterized; then the conditions under which a Lie higher derivation on generalized matrix algebras is proper…

We study the space of derivations for some finite-dimensional evolution algebras, depending on the twin partition of an associated directed graph. For evolution algebras with a twin-free associated graph we prove that the space of…

I. P. Goulden, S. Litsyn, and V. Shevelev [On a sequence arising in algebraic geometry, J. Integer Sequences 8 (2005), 05.4.7] conjectured that certain Laurent polynomials associated with the solution of a functional equation have only odd…