Related papers: Inner and Outer Derivations of $\mathbb{F}V_{8n}$

A series of associative algebras $A_n(V)$ for a vertex operator algebra $V$ over an arbitrary algebraically closed field and nonnegative integers $n$ are constructed such that there is a one to one correspondence between irreducible…

A fully irreducible outer automorphism phi of the free group F_n of rank n has an expansion factor which often differs from the expansion factor of the inverse of phi. Nevertheless, we prove that the ratio between the logarithms of the…

Given a von Neumann algebra $M$ with a faithful normal semi-finite trace $\tau,$ let $L(M, \tau)$ be the algebra of all $\tau$-measurable operators affiliated with $M.$ We prove that if $A$ is a locally convex reflexive complete metrizable…

We study the outer automorphism group of a right-angled Artin group $A_\Gamma$ with finite defining graph $\Gamma$. We construct a subnormal series for $Out(A_\Gamma)$ such that each consecutive quotient is either finite, free-abelian,…

Let $p$ be a prime and let $G$ be a finite $p$-group. We show that the isomorphism type of the maximal abelian direct factor of $G$, as well as the isomorphism type of the group algebra over $\mathbb F_p$ of the non-abelian remaining direct…

Let $G$ be a finite group and $H$ a normal subgroup of prime index $p$. Let $V$ be an irreducible ${\mathbb F}H$-module and $U$ a quotient of the induced ${\mathbb F}G$-module $V\kern-3pt\uparrow$. We describe the structure of $U$, which is…

The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…

We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a…

We define and compute $\operatorname{ABrd}_p(F)$, the asymptotic Brauer $p$-dimension of a field $F$, in cases where $F$ is a rational function field or Laurent series field. $\operatorname{ABrd}_p(F)$ is defined like the Brauer…

We prove that an iterative derivation $\delta_F$ on a field $F$ can be extended to an iterative derivation $\delta_A$ on a central simple $F-$algebra $A$ if the characteristic of $F$ does not divide the exponent of $A$ in the Brauer group…

Let $\mathbb F$ be a field $\mathbb F $ of characteristic zero. Let $W_{n}(\mathbb F)$ be the Lie algebra of all $\mathbb F$-derivations with the Lie bracket $[D_1, D_2]:=D_1D_2-D_2D_1$ on the polynomial ring $\mathbb F [x_1, \ldots ,…

We study a series of real nonassociative algebras $\mathbb{O}_{p,q}$ introduced in $[5]$. These algebras have a natural $\mathbb{Z}_2^n$-grading, where $n=p+q$, and they are characterized by a cubic form over the field $\mathbb{Z}_2$. We…

Let $A$ be Banach algebra over commutative ring $D$. The map $f:A\rightarrow A\ $ is called differentiable in the Gateaux sense, if $$f(x+a)-f(x)=\partial f(x)\circ a+o(a)$$ where the Gateaux derivative $\partial f(x)$ of map $f$ is linear…

An automorphism of a group is called outer if it is not an inner automorphism. Let $G$ be a finite $p$-group. Then for every outer $p$-automorphism $\phi$ of $G$ the subgroup $C_G(\phi)=\{x\in G \;|\; x^\phi=x\}$ has order $p$ if and only…

Let $k$ be a field containing an algebraically closed field of characteristic zero. If $G$ is a finite group and $D$ is a division algebra over $k$, finite dimensional over its center, we can associate to a faithful $G$-grading on $D$ a…

Let $p$ be a prime integer, $1\leq s\leq r$ integers, $F$ a field of characteristic $p$. Let $\cat{Dec}_{p^r}$ denote the class of the tensor product of $r$ $p$-symbols and $\cat{Alg}_{p^r,p^s}$ denote the class of central simple algebras…

In this paper we study the existence of at least one non-inner automorphism of order p of a non-abelian finite p-group of coclass 3, where p is a prime integer such that p is different from 3.

Let $\mathcal{A} = {A_1, ..., A_k}$ be a system of free factors of $F_n$. The group of relative automorphisms $\mathrm{Aut}(F_n; \mathcal{A})$ is the group given by the automorphisms of $F_n$ that restricted to each $A_i$ are conjugations…

We classify the four dimensional perfect non-simple evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.

The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash…