Virasoro代数同构的不可约表示

Ｖｉｒａｓｏｒｏ代数同构的不可约表示赵开明（中国科学院系统科学研究所，北京１０００８０）１９９０年１２月４日收到，１９９３年４月２８日收到修改稿．Ｖｉｒａｓｏｒｏ代数的表示理论在数学和物理的许多分支中起着重要的作用，例如在仿射Ｌｉｅ代数理论［１，２］...     

广义Virasoro-Toroidal李代数不可约模

本文将Kac-Moody代数A(1)1的二阶表示理论[11]推广到Toroidal李代数的情形.并给出了A1型Toroidal李代数的一类不可约表示.     

广义Virasoro-Toroidal李代数不可约模

本文将Kac-Moody代数A1（1）的二阶表示理论[11]推广到Toroidal李代数的情形.并给出了A1型Toroidal李代数的一类不可约表示.     

一类格序半群的同余

本文讨论了一类可换格序半群的同余性质。给出了这类格序半群同余的表示和同态分解定理。这个结论一般化了［１］和［２］中的结果。     

IRREDUCIBLE REPRESENTATIONS FOR THE AFFINE-VIRASORO LIE ALGEBRA OF TYPE B_l

An explicit construction of irreducible representations for the affine-Virasoro Liealgebra of type B_l, through the use of vertex operators and certain oscillator represen-tations of the Virasoro algebra, is given.     

AUTOMORPHISMS OF THE ENVELOPING ALGEBRA OF THE THREE-DIMENSIONAL NILPOTENT LIE ALGEBRA

We prove that the group of tame automorphisms of the universal enveloping algebra of the three-dimensional nilpotent nonabelian Lie algebra over a field of characteristic 0 is dense with respect to the formal power series topology in the group of all automorphisms.

     

A NOTE ON A TRANSFERENCE THEOREM OF THE SYSTEMS OF LINEAR CONGRUENCES

<正> Let p be a prime number. Let a_(ij)(1≤i≤t,1≤j≤s) be a set of st integers.Weuse the notations x=max(1, |x|), p_1=[(p-1)/2], p_2=[p/2], and (a)_p to denote the integer satisfying (a)_p=a(mod p),-p_1≤(a)_p≤p_2. Consider the dual of linear congruences     

THE REGULAR COMPONENTS OF THE AUSLANDER-REITEN QUIVER OF A TILTED ALGEBRA

Let B be a connected finite-dimensional hereditary algebra of infinite representationtype.It is shown that there exists a regular tilting B-module if and only if B is wild andhas at least three simple modules.In this way,the author determines the possible form ofregular components which arise as a connecting component of the Auslander-Reitenquiver Γ(A)of a tilted algebra A.The second result asserts that for a tilted algebra A,any regular component of Γ(A)which is not a connecting component,is quasi-serial.     

关于有限群的不可约特征标个数的一个结果

本文研究了一般的非交换有限群G的阶与不可约特征标个数的比值与群G结构之间的关系.通过群G阶的最小素因子和G的换位子群的阶的最小素因子,得出了这个比值的下界,并确定了达到下界的一个充分必要条件.     

A NEW EXTENSION OF THE HIGH-ORDER VIRASORO ALGEBRA

1 IntroductionVirasoro algebra and W algebra have been widely investigated by both physicists andmahematicians. Virasoro algebra can be thought of as the central extended algebra Of diffeOmorphisms Di$S') on the circle S1. In Ref[1], ftaPpat et al. extended the notion ofloop algebra g(S') to algebra g(M), M being a closed surface with dim M > 1, and gave thefolowing commutation relations:c,[Lk,l, L.,.] = [mp(k -- T) -- ftO(l -- 8)]Lk .,l , ti ll ghO(k -- j) -- fl0(l -- j)lok .,O8l ,,…     

THE SEMICENTRE OF A GROUP ALGEBRA. II

The semicentre of an arbitrary group algebra K[G] is studied. In particular necessary and sufficient conditions are shown such that the semicentre is equal to a fixed subring of K[Δ(G)]. Also the semicentre is always equal to a sum of centres of certain subgroup algebras.     

三项式xn-x-a的二次不可约因式

设n是正整数,f(x)=xn-x-a,其中a是非零整数. 证明了当n>5时,如果f(x)有首项系数为1的二次整系数不可约因式g(x),则必有n≡2(mod6),a=-1,g(x)=x2-x+1或者n=7,a=±280,g(x)=x2t(±)x+5.     

格序群的扭自由根式格

证明了发下结果；格序群的扭自由根式全体构成一个完备格县这个格满足并无限分配律，所有主扭自由根式构成这个格的一个理想。     

无限维Heisenberg代数的导子代数和全形

给出了无维Ｈｅｉｓｒｂｅｒｇ代数的全形和全形的导子代数Ｄｅｒ（ｓ）证明（ｓ）不是一个完备李代数，但Ｄｅｒ（ｓ）是一个完备李代数。     

ON THE SPECTRAL RADIUS OF IRREDUCIBLE AND WEAKLY IRREDUCIBLE OPERATORS IN BANACH LATPICES

Abstract

If T is an operator on a Banach lattice E we call T weakly irreducible if E contains no non-trivial T-invariant bands. We prove that if E is order complete and if the weakly irreducible operator T > 0 is in (E′_oo ? E)^⊥⊥ then T has positive spectral radéus. Prom this follows that Jentesch's theorem holds in arbitrary Banach function spaces.

If [Ttilde] denotes the restriction of T′ to E′_oo, 0 ? T an order continuous operator, then T is weakly irreducible if and only if [Ttilde]: E′_oo→E′_oo is weakly irreducible.

Finally we show that the majorizing, irreducible operator T ≥ 0, has positive spectral radius if either Tⁿ is weakly compact or E has property (P) or T is strongly majorizing.     

半群的半直积及其同余

给出了两个幺半群的半直积是Ｃｌｉｆｏｒｄ半群的充要条件及其结构．并讨论了逆半群半直积的Ｇｒｅｅｎ关系、最小群同余和极大幂等元分离同余．     

有理样条不可约解的行列式表示

１引言在文［１］中,对于剖分ａ＝ｘ０＜ｘ１＜…＜ｍｎ＝ｂ及给定的ｙ０,ｙ１,…,　…,Ｌ＋Ｍ－１,我们构造了有理样条Ｓ［Ｌ,Ｍ（ｘ）Ｑ［Ｌ,Ｍ］为次数不超过ｍ的多项式全体．在［１］中,已经讨论了Ｓ［Ｌ,Ｍ］（ｘ）的存在性,并指出：若问题（１）（２）（３）可解,则解唯一这里总假设问题（１）（２）（３）可解．２有理样条解不可约的充要条件由Ｓ［Ｌ,Ｍ］（ｘ）的依区间递推算法（见［１］）,我们只需讨论［ｘ０,ｘ１］上的情形．当［Ｘ０,ｘ１］时,将Ｓ［Ｌ,Ｍ］　（ｘ）,Ｐ［Ｌ,Ｍ］　（ｘ）和Ｑ［Ｌ,Ｍ］（…     

THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS

1. Notations and Basic ResultsLet G be a finite nonabelian group. Then frs(G/G') is an abelian group under themultiplication of characters and acts on the set of non-linear irreducible characters of G viathe multiplication of characters. The purpose of this paper is to investigate this action. Asan application of our theoryl in the end of Section 3 we give the classification of groupshaving exactly three non-linear irreducible caracters.All groups in the paper are finite. For a factor grou…