Related papers: Domains in $\cx {n+1}$ with Noncompact Automorphis…

The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.

We exhibit normal subgroups of a free nilpotent group F of rank two and class three, which have isomorphic finite quotients but are not conjugate under any automorphism of F.

We compute the virtual cohomological dimension (VCD) of the group of partially symmetric outer automorphisms of a free group. We use this to obtain new upper and lower bounds on the VCD of the outer automorphism group of a two-dimensional…

We develop techniques for computing the AK invariant of a domain with arbitrary characteristic. We use these techniques to describe for any field $K$ the automorphism group of $K[X,Y,Z]/(X^n Y - Z^2 - h(X)Z)$, where $h(0) \ne 0$ and $n \geq…

We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

In this paper we determine the automorphism group of the Fock-Bargmann-Hartogs domain $D_{n,m}$ in $\mathbb{C}^n\times\mathbb{C}^m$ which is defined by the inequality ${\|\zeta\|}^2<e^{-\mu{\|z\|}^2}$.

We study holomorphic self-maps of non-ordered n-point configuration spaces C^n(X), where X is either affine or projective complex line. The complex Lie group Aut(X) acts diagonally on C^n(X). We prove that for n>4 every endomorphism F of…

We consider the infinite-dimensional hypercube graph. This graph is not connected and has isomorphic connected components. We describe the restrictions of its automorphisms to the connected components and the automorphism group of connected…

See math.CV/0509030 which replaces this paper.

We give a "limit-free formula" simplifying the computation of the topological entropy for topological automorphisms of totally disconnected locally compact groups. This result allows us to extend several basic properties of the topological…

This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…

A survey article that presents some recent algebraic and model-theoretic results on the automorphism groups of relatively free groups of infinite rank. The topics include topological aspects, generating sets, descripition of automorpisms…

Any non-abelian finite $p$-group has a non-inner automorphism of order $p$.

We obtain a complete classification of hypercomplex manifolds, on which a compact group of automorphisms acts transitively. The description of the spaces as well as the proofs of our results use only the structure theory of reductive…

We present some results in the analysis of non-compact differential equations on unbounded domains.

The aim of this note is to explain a generalization to the real case of a well known result on the automorphism group of an unbounded tube type symmetric domain in a complex vector space of finite dimension.

For n >2, we shall show that the group Aut(NS(M)) of simplicial automorphisms of the complex NS(M) of non-separating embedded spheres in the manifold M,connected sum of n copies of S^2 X S^1, isomorphic to the group Out(F_n) of outer…

We compute the automorphism group of the dual complex $\mathsf{T}_{d, n}$ of the boundary divisor in the Kontsevich moduli space $\overline{\mathcal{M}}_{0, n}(\mathbb{P}^r, d)$. When $d \geq 2$, we find that $\mathrm{Aut}(\mathsf{T}_{d,…

We shall explain here an idea to generalize classical complex analytic Kleinian group theory to any odd dimensional cases. For a certain class of discrete subgroups of $\PGL_{2n+1}(\C)$ acting on $\P^{2n+1}$, we can define their domains of…

We survey some results and questions about free actions of infinite groups on products of spheres and euclidean spaces, and give some new co-compact examples.