Related papers: Automorphisms of central extensions of type I von …

We obtain a recurrent and monotone method for constructing and classifying nilpotent Lie algebras by means of successive central extensions. It consists in calculating the second cohomology of an extendable nilpotent Lie algebra with the…

In this paper we prove that any local automorphism on the solvable Leibniz algebras with null-filiform and naturally graded non-Lie filiform nilradicals, whose dimension of complementary space is maximal is an automorphism. Furthermore, the…

We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…

Let $\phi \in \mbox{Out}(F_n)$ be a free group outer automorphism that can be represented by an expanding, irreducible train-track map. The automorphism $\phi$ determines a free-by-cyclic group $\Gamma=F_n \rtimes_\phi \mathbb Z,$ and a…

This paper is devoted to local derivations on subalgebras on the algebra $S(M, \tau)$ of all $\tau$-measurable operators affiliated with a von Neumann algebra $M$ without abelian summands and with a faithful normal semi-finite trace $\tau.$…

We investigate the general structure of the automorphism group and the Lie algebra of derivations of a finitely generated vertex operator algebra. The automorphism group is isomorphic to an algebraic group. Under natural assumptions, the…

Let {\phi} be an automorphism on a connected Lie group G. Through several G-subgroups associated to the dynamics of {\phi} we analyze their topological entropy. Assume that G belongs to the class of finite semisimple center Lie groups which…

We study automorphisms $\alpha$ of a totally disconnected, locally compact group $G$ which are expansive in the sense that, for some identity neighbourhood $U$, the sets $\alpha^n(U)$ (for integers $n$) intersect in the trivial group.…

We show that every ring isomorphism between the algebras of locally measurable operators for type II$_\infty$ von Neumann algebras is similar to a real $^*$-isomorphism. This together with previous results by the author and…

We obtain some results that relate the Connes spectrum with the innerness of automorphisms in the fixed point local multiplier algebra. The results are variants and/or extensions of corresponding results of Olesen, Pedersen and Stormer [6],…

Every transformation monoid comes equipped with a canonical topology-the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This…

An automorphism of a graph $G=(V,E)$ is a bijective map $\phi$ from $V$ to itself such that $\phi(v_i)\phi(v_j)\in E$ $\Leftrightarrow$ $v_i v_j\in E$ for any two vertices $v_i$ and $v_j$. Denote by $\mathfrak{G}$ the group consisting of…

Let $q$ be an algebraic Lie algebra and $q<m>$ a (generalised) Takiff algebra. Any finite order automorphism $\theta$ of $q$ induces an automorphisms of $q<m>$ of the same order, denoted $\Theta$. We study invariant-theoretic properties of…

Glimm's theorem says that a UHF algebra is almost embedded in a separable $C^*$-algebra not of type I. Applying his methods we obtain a covariant version of his result; a UHF algebra with a product type automorphism is covariantly embedded…

Given a type I von Neumann algebra $M$ with a faithful normal semi-finite trace $\tau,$ let $S_0(M, \tau)$ be the algebra of all $\tau$-compact operators affiliated with $M.$ We give a complete description of all derivations on the algebra…

Let $\{\phi_s\}_{s\in S}$ be a commutative semigroup of completely positive, contractive, and weak*-continuous linear maps acting on a von Neumann algebra $N$. Assume there exists a semigroup $\{\alpha_s\}_{s\in S}$ of weak*-continuous…

A loop is automorphic if all its inner mappings are automorphisms. We construct a large family of automorphic loops as follows. Let $R$ be a commutative ring, $V$ an $R$-module, $E=\mathrm{End}_R(V)$ the ring of $R$-endomorphisms of $V$,…

A loop whose inner mappings are automorphisms is an \emph{automorphic loop} (or \emph{A-loop}). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this characterization and certain…

We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when edge groups are cyclic, and vertex groups are torsion-free with cyclic centralizers. We show that in this case the outer automorphism group…

Let $F$ be a perfect field and $M^*(F)$ the nonassociative simple Moufang loop consisting of the units in the (unique) split octonion algebra $O(F)$ modulo the center. Then $Aut(M^*(F))$ is equal to $G_2(F) \rtimes Aut(F)$. In particular,…