On automorphisms of finite Abelian <Emphasis Type="Italic">p</Emphasis>-groups

Let A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A _p . For a finite abelian p-group A of type (k ₁, ..., k _n ), simple necessary and sufficient conditions for an n × n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k ₁, k ₂) is analyzed. This work has begin during the visit of the second author to the Faculty of Mathematics and Computer Science, Nicolaus Copernicus University during the period July 31–August 13, 2005. This visit was supported by the Nicolaus Copernicus University and a grant from Cnpq.     

Elementary equivalence for the lattices of subalgebras and automorphism groups of free algebras

We find an elementary equivalence criterion for the lattices of subalgebras of free algebras in regular varieties. The question is addressed of elementary equivalence for the automorphism groups of algebras of this type.     

Fano varieties with many selfmaps

We study global log canonical thresholds of anticanonically embedded quasismooth weighted Fano threefold hypersurfaces having terminal quotient singularities to prove the existence of a Kähler-Einstein metric on most of them, and to produce examples of Fano varieties with infinite discrete groups of birational automorphisms.     

^3D4（q）群与射影平面

本文证明若^3D4（q）△G≤Aut（^3D4（q）），这里q是素数方幂，则G不能点传递作用在一个射影平面上.     

两类重要p-群及其自同构群的阶

In the paper we obtain two infinite classes of p-groups,calculate the orders of their automorphism groups and correct a mistake(perhaps misprinted)of Rodney James'paper in 1980.     

Counting the number of indecomposable representations and a q-analogue of the Weyl-Kac denominator identity of type _n

By using Frobenius maps and F-stable representations,we count the number of isomor- phism classes of indecomposable representations with the fixed dimension vector of a species of type _n over a finite field,first,and then,as an application,give a q-analogue of the Weyl-Kac denominator identity of type _n.     

Every compact group arises as the outer automorphism group of a II1 factor

We show that any compact group can be realized as the outer automorphism group of a factor of type II₁. This has been proved in the abelian case by Ioana, Peterson and Popa [A. Ioana, J. Peterson, S. Popa, Amalgamated free products of w-rigid factors and calculation of their symmetry group, math.OA/0505589, Acta Math., in press] applying Popa's deformation/rigidity techniques to amalgamated free product von Neumann algebras. Our methods are a generalization of theirs.     

Transversal infinitesimal automorphisms of harmonic foliations on complete manifolds

Summary In this paper we study infinitesimal automorphisms of finiteL ²-norm for harmonic Riemannian and Kähler foliations admitting a complete bundle-like metric. The results generalize facts established recently in the compact case.1980 Mathematics Subject Classification: Primary 57 R 30, Secondary 58 E 20.Work supported in part by a grant from the National Science Foundation.     

Coleman自同构群的投射极限

在这篇注记中，利用群的投射极限性质给出了有限可解群的Coleman自同构群的一个具体构造.作为应用，证明了二面体群的Coleman外自同构群或者是1或者是一个初等阿贝尔2-群.     

Supersymmetric invariance and universal central extensions of lie supertriple systems

In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland's theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.