A NOTE ON COMMUTING SQUARES ARISING FROM AUTOMORPHISMS ON SUBFACTORS

1999 ◽  
Vol 10 (02) ◽  
pp. 207-214 ◽  
Author(s):  
PHAN H. LOI
Keyword(s):  
Finite Index ◽  
Simple Proof ◽  
Classification Theorem ◽  
Type Ii ◽  
Finitely Generated ◽  
Amenable Groups ◽  
Finite Set ◽  
Commuting Squares ◽  
Special Case

Using an idea due to Popa, we can associate a commuting square of factors to any given finite set of automorphisms acting on an inclusion of factors of finite index. We use this setting to obtain a simple proof of Popa's classification theorem of strongly outer actions of finitely generated discrete strongly amenable groups on a strongly amenable inclusion of type II 1 factors. We also obtain a new complete outer conjugacy invariant for arbitrary automorphisms, which contains the higher obstruction of Kawahigashi and the standard invariant as a special case.

scholarly journals An embedding theorem for fields

1976 ◽  
Vol 14 (2) ◽  
pp. 193-198 ◽  
Author(s):  
J.W.S. Cassels
Keyword(s):  
Simple Proof ◽  
Embedding Theorem ◽  
Normal Subgroups ◽  
Finitely Generated ◽  
Matrix Groups ◽  
Recurrent Sequences ◽  
Finite Set ◽  
Torsion Free

It is shown that every finitely generated field K of characteristic 0 may be embedded in infinitely many p-adic fields in such a way that the images of any given finite set C of non-zero elements of K are p-adic units. The result is suggested by Lech's proof of his generalization of Mahler's theorem on recurrent sequences. It also provides a simple proof of Selberg's theorem about torsion-free normal subgroups of matrix groups.

CLASSIFICATION OF APPROXIMATELY INNER ACTIONS OF DISCRETE AMENABLE GROUPS ON STRONGLY AMENABLE SUBFACTORS

2005 ◽  
Vol 16 (10) ◽  
pp. 1193-1206 ◽  
Author(s):  
TOSHIHIKO MASUDA
Keyword(s):  
Classification Theorem ◽  
Type Ii ◽  
Amenable Groups ◽  
Characteristic Invariant

We give the classification theorem of approximately inner actions of discrete amenable groups on strongly amenable subfactor of type II1by means of the characteristic invariant and ν invariant. To prove this theorem, we also give the classification theorem when the inner part and the centrally trivial part of actions coincide.

STRONGLY FREE ACTIONS ON SUBFACTORS

1993 ◽  
Vol 04 (04) ◽  
pp. 675-688 ◽  
Author(s):  
CARL WINSLØW
Keyword(s):  
Finite Index ◽  
Algebraic Property ◽  
Type Ii ◽  
Amenable Groups ◽  
Type Iii ◽  
Cocycle Conjugacy ◽  
Free Actions

For actions on arbitrary inclusions of factors with finite index, we define an algebraic property called "strong freeness". In the case of strongly amenable subfactors of type II∞ or IIIλ (0 < λ < 1), this property is shown to be a characterization of centrally free actions. We then classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type II∞, and strongly free actions of a class of discrete amenable groups (which include ℤn, n ∈ ℕ) on strongly amenable subfactors of type IIIλ. Namely, we show that the (generalized) fundamental homomorphism is a complete invariant for cocycle conjugacy in both cases.

Automorphisms of finite order of nilpotent groups II

2014 ◽  
Vol 51 (4) ◽  
pp. 547-555 ◽  
Author(s):  
B. Wehrfritz
Keyword(s):  
Nilpotent Group ◽  
Finite Order ◽  
Finite Index ◽  
Nilpotent Groups ◽  
Finitely Generated

Let G be a nilpotent group with finite abelian ranks (e.g. let G be a finitely generated nilpotent group) and suppose φ is an automorphism of G of finite order m. If γ and ψ denote the associated maps of G given by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma :g \mapsto g^{ - 1} \cdot g\phi and \psi :g \mapsto g \cdot g\phi \cdot g\phi ^2 \cdots \cdot \cdot g\phi ^{m - 1} for g \in G,$$ \end{document} then Gγ · kerγ and Gψ · ker ψ are both very large in that they contain subgroups of finite index in G.

Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups

2021 ◽  
pp. 1-36
Author(s):  
ARIE LEVIT ◽  
ALEXANDER LUBOTZKY
Keyword(s):  
Ergodic Theorem ◽  
Abelian Groups ◽  
Wreath Products ◽  
Finitely Generated ◽  
Metabelian Groups ◽  
Amenable Groups ◽  
Pointwise Ergodic Theorem ◽  
Lamplighter Group ◽  
Invariant Random Subgroups

Abstract We prove that all invariant random subgroups of the lamplighter group L are co-sofic. It follows that L is permutation stable, providing an example of an infinitely presented such group. Our proof applies more generally to all permutational wreath products of finitely generated abelian groups. We rely on the pointwise ergodic theorem for amenable groups.

scholarly journals On the Bean critical-state model in superconductivity

1996 ◽  
Vol 7 (3) ◽  
pp. 237-247 ◽  
Author(s):  
L. Prigozhin
Keyword(s):  
Variational Inequalities ◽  
Critical State ◽  
Existence And Uniqueness ◽  
Critical State Model ◽  
Type Ii ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Uniqueness Of The Solution ◽  
Type Ii Superconductivity ◽  
Special Case

We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

SH pulse in an elastic wedge

1973 ◽  
Vol 63 (5) ◽  
pp. 1571-1582
Author(s):  
A. M. Abo-Zena ◽  
Chi-Yu King
Keyword(s):  
Integral Transform ◽  
Wedge Angle ◽  
Integral Form ◽  
Diffraction Effect ◽  
Elastic Wedge ◽  
Sh Waves ◽  
Wedge Surface ◽  
Line Parallel ◽  
Finite Set ◽  
Special Case

abstract This paper gives an analysis of the response of an elastic wedge of arbitrary angle to an impulsive SH source applied on the wedge surface along a line parallel to the edge of the wedge. A two-dimensional time-dependent Green's function for SH waves is constructed from an integral-transform approach. The result is given in a closed form for the incident and the reflected pulses and in an integral form for the diffracted pulse from the edge. For the special case that the wedge angle is an integral fraction of π, the result is interpretable in terms of a finite set of image sources with no diffraction effect. Numerical examples are given for illustration.

scholarly journals Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups

2015 ◽  
Vol 58 (4) ◽  
pp. 787-798 ◽  
Author(s):  
Yu Kitabeppu ◽  
Sajjad Lakzian
Keyword(s):  
Diameter Growth ◽  
Fundamental Groups ◽  
Finitely Generated ◽  
Finite Generation ◽  
Alexandrov Spaces ◽  
Geodesic Spaces ◽  
Special Case ◽  
Linear Diameter

AbstractIn this paper, we generalize the finite generation result of Sormani to non-branching RCD(0, N) geodesic spaces (and in particular, Alexandrov spaces) with full supportmeasures. This is a special case of the Milnor’s Conjecture for complete non-compact RCD(0, N) spaces. One of the key tools we use is the Abresch–Gromoll type excess estimates for non-smooth spaces obtained by Gigli–Mosconi.

ON THE RANK OF ABELIAN VARIETIES OVER AMPLE FIELDS

2010 ◽  
Vol 06 (03) ◽  
pp. 579-586 ◽  
Author(s):  
ARNO FEHM ◽  
SEBASTIAN PETERSEN
Keyword(s):  
Finite Field ◽  
Abelian Variety ◽  
Galois Extension ◽  
Characteristic Zero ◽  
Rational Point ◽  
Abelian Varieties ◽  
Finitely Generated ◽  
Infinite Rank ◽  
Finite Set

A field K is called ample if every smooth K-curve that has a K-rational point has infinitely many of them. We prove two theorems to support the following conjecture, which is inspired by classical infinite rank results: Every non-zero Abelian variety A over an ample field K which is not algebraic over a finite field has infinite rank. First, the ℤ(p)-module A(K) ⊗ ℤ(p) is not finitely generated, where p is the characteristic of K. In particular, the conjecture holds for fields of characteristic zero. Second, if K is an infinite finitely generated field and S is a finite set of local primes of K, then every Abelian variety over K acquires infinite rank over certain subfields of the maximal totally S-adic Galois extension of K. This strengthens a recent infinite rank result of Geyer and Jarden.

Ε‎-Fr ´Echet Differentiability

2012 ◽  
Author(s):  
Joram Lindenstrauss ◽  
David Preiss ◽  
Tiˇser Jaroslav
Keyword(s):  
Banach Space ◽  
Convex Hull ◽  
Simple Proof ◽  
Common Point ◽  
Lipschitz Functions ◽  
Closed Convex Hull ◽  
Uniformly Smooth ◽  
Fréchet Differentiability ◽  
Finite Set ◽  
Frechet Differentiability

This chapter treats results on ε‎-Fréchet differentiability of Lipschitz functions in asymptotically smooth spaces. These results are highly exceptional in the sense that they prove almost Frechet differentiability in some situations when we know that the closed convex hull of all (even almost) Fréchet derivatives may be strictly smaller than the closed convex hull of the Gâteaux derivatives. The chapter first presents a simple proof of an almost differentiability result for Lipschitz functions in asymptotically uniformly smooth spaces before discussing the notion of asymptotic uniform smoothness. It then proves that in an asymptotically smooth Banach space X, any finite set of real-valued Lipschitz functions on X has, for every ε‎ > 0, a common point of ε‎-Fréchet differentiability.

Sign in / Sign up

Export Citation Format

Share Document