Related papers: Automorphisms of unstable ${\mathbb P}^1$-bundles

Apart from math.AG/0608569, it contains the following applications of it. Let M be a simply connected, irreducible smooth complex projective variety of dimension $n$ such that the Picard number of $M$ is one. If the canonical line bundle…

Let G be a connected algebraic group over an algebraically closed field of characteristic p (possibly 0), and X a variety on which G acts transitively with connected stabilizers. We show that any \'etale Galois cover of X of degree prime to…

If B is C*-algebra of finite dimension n>3 then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say G, have the same fusion rules as the ones of SO(3). As consequences, we get (1) a…

The paper follows two interconnected directions. 1. Let $G$ be a Roelcke precompact closed subgroup of the group $\Sym(\omega)$ of permutations of the natural numbers. Then $\Inn(G)$ is closed in $\Aut(G)$, where $\Aut(G)$ carries the…

Consider a tree $\mathbb T$, all whose vertices have countable valence; its boundary is the Baire space $\mathbb{B} \simeq\mathbb{N}^{\mathbb N}$; continued fractions expansions identify the set of irrational numbers $\mathbb{R}\setminus…

Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms, we first prove some results on the solvability of finite groups in which some maximal $A$-invariant subgroups have indices a prime or the square of a…

The aim of this paper is to give verifiable criteria for the existence of {\em irreducible} homomorphisms of $\pi_{1}(\mathbb P^1 - \mathcal R)$ into compact semisimple groups, for a finite subset $\mathcal R$ such that the conjugacy…

It is a well-known fact that every group $G$ has a presentation of the form $G = F/R$, where $F$ is a free group and $R$ the kernel of the natural epimorphism from $F$ onto $G$. Driven by the desire to obtain a similar presentation of the…

Let $R$ be an integral domain over a field $k$, and $G$ a subgroup of the automorphism group of the polynomial ring $R[x_1,..., x_n]$ over $R$. In this paper, we discuss when $G$ is diagonalizable under the assumption that $G$ is…

For any abstract subfactor planar algebra $P$, there exists a finite index extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In this paper, we classify the automorphism group of a bipartite graph planar algebra, and…

We define what is meant by a strict total order in a category having subobjects, products and fibre products. This allows us to define the notions of an ordered bundle X and an ordered G-set; when G=\pi_1(X) we relate these structures to…

It is shown that a flat subgroup, $H$, of the totally disconnected, locally compact group $G$ decomposes into a finite number of subsemigroups on which the scale function is multiplicative. The image, $P$, of a multiplicative semigroup in…

For any algebraically closed field $K$ and any endomorphism $f$ of $\mathbb{P}^1(K)$ of degree at least 2, the automorphisms of $f$ are the M\"obius transformations that commute with $f$, and these form a finite subgroup of…

If a finite group $A$ acts coprimely as automorphisms on a finite group $G$, then the $A$-invariant Brauer $p$-blocks of $G$ are exactly those that contain $A$-invariant irreducible characters.

An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. For…

The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.

Suppose that $B$ is a $G$-Banach algebra over $\mathbb{F} = \mathbb{R}$ or $\mathbb{C}$, $X$ is a finite dimensional compact metric space, $\zeta : P \to X$ is a standard principal $G$-bundle, and $A_\zeta = \Gamma (X, P \times_G B)$ is the…

Let M be an irreducible smooth projective variety defined over \bar{{\mathbb F}_p}. Let \pi(M, x_0) be the fundamental group scheme of M with respect to a base point x_0. Let G be a connected semisimple linear algebraic group over…

Let $G$ be a group. The central automorphism group $Aut_c(G)$ of $G$ is the centralizer of $Inn(G)$ the subgroup of $Aut(G)$ of inner automorphisms. There is a one to one map $ \sigma \mapsto h_\sigma$ from the set $Aut_c(G)$ onto the set…

Let $X$ be an irreducible smooth complex projective variety. Let $G$ be a linear algebraic group over $\mathbb{C}$. We define the notion of Lie algebroid valued connection on holomorphic principal $G$--bundles on $X$, and study their basic…