关于单BCI－代数的一些结果

本文讨论了单ＢＣＩ－代数．证明了一个ＢＣＩ－代数是单的当且仅当它的子代数都是单的；给出了单ｐ－半单ＢＣＩ－代数的一种表示式；证明了一个ｐ－半单ＢＣＩ－代数是单的当且仅当它的阶是素数；这样得到了一批（无限多个）单ＢＣＩ－代数；证明了商ＢＣＫ－代数Ｘ／Ａ是单的当且仅当Ａ是Ｘ的极大理想．     

Classification of simple weight Virasoro modules with a finite-dimensional weight space

We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite-dimensional. As a corollary we obtain that every simple weight module over the Virasoro algebra, having a non-trivial finite-dimensional weight space, is a Harish-Chandra module (and hence is either a simple highest or lowest weight module or a simple module from the intermediate series). This implies positive answers to two conjectures about simple pointed and simple mixed modules over the Virasoro algebra.     

On Real Simple Left-symmetric Algebras

In this article, we commence to study the real (simple) left-symmetric algebras. From the known classification of certain complex (semi)simple left-symmetric algebras, we classify their corresponding real forms. We not only obtain the classification of real simple left-symmetric algebras in low dimensions, but also find certain examples of real simple left-symmetric algebras in higher dimensions. In particular, there exists a complex simple left-symmetric algebra without any real form. We also give a geometric construction for a class of real simple left-symmetric algebras. At last, we apply the classification results to study some structures related to geometry.     

Effectivity functions and simple games

The rather new notion of effectivity function is related to the notion of simple game. Every effectivity function is associated with a simple game. So theory about simple games may be applicable to effectivity functions. E.g. if the effectivity function is additive, then the associated simple game is weighted. Via a characterization of weighted simple games it is possible to characterize maximal additive effectivity functions.Finally we characterize additive effectivity functions and their associated simple games.I thank G.J. Otten for useful comments and stimulating conversations.     

Hopf箭图与Hopf代数

本文研究了简单无向Hopf箭图的图论性质以及路代数与路余代数的关系.利用简单无向Hopf箭图与简单图的关系.证明了路代数是路余代数的对偶的直和部分.     

Local and Subquotient Inheritance of Simplicity in Jordan Systems

In this paper we prove that the local algebras of a simple Jordan pair are simple. Jordan pairs all of which local algebras are simple are also studied, showing that they have a nonzero simple heart, which is described in terms of powers of the original pair. Similar results are given for Jordan triple systems and algebras. Finally, we characterize the inner ideals of a simple pair which determine simple subquotients, answering the question posed by O. Loos and E. Neher (1994, J. Algebra166, 255–295).     

Simple systems and their higher order self-joinings

The purpose of this work is to study the joinings of simple systems. First the joinings of a simple system with another ergodic system are treated; then the pairwise independent joinings of three systems one of which is simple. The main results obtained are: (1) A weakly mixing simple system with no non-trivial factors with absolutely continuous spectral type is simple of all orders. (2) A weakly mixing system simple of order 3 is simple of all orders.     

The desirability relation of simple games

We prove some properties of simple games with a complete desirability relation, and investigate the relationships between the desirability of a simple game G and that of some simple games that are derived from G. We also provide an example of a proper simple game that has a complete and acyclic desirability relation but is not a weighted majority game.     

Traces on simple AF C1-algebras

The relations between the set of traces on a simple approximately finite dimensional C¹-algebra A and the algebraic and geometric properties of the Elliott dimension group K₀(A) are studied. It is shown that every metrizable Choquet simplex occurs as the set of normalized traces of a simple unital AF algebra. A simple AF algebra can have both finite and infinite traces, so a finite simple AF algebra need not be algebraically simple. It is shown that a simple AF algebra is algebraically simple if and only if it has no infinite traces, and is stable if and only if it has no finite traces.     

关于单$K_4-$群的新刻画

本文用群阶和高阶元素的阶刻画了部分单$K_4-$群. 所谓单$K_4$-群就是其阶只含4个素因子的单群.     

Non-embeddable simple relation algebras

This paper presents solutions or partial solutions for several problems in the theory of relation algebras. In a simple relation algebra an element x satisfying the condition (a) must be an atom of . It follows that x must also be an atom in every simple extension of . Andréka, Jónsson and Németi [1, Problem 4] (see [12, Problem P5]) asked whether the converse holds: if x is an atom in every simple extension of a simple relation algebra, must it satisfy (a)? We show that the answer is “no”.? The only known examples of simple relation algebras without simple proper extensions are the algebras of all binary relations on a finite set. Jónsson proposed finding all finite simple relation algebras without simple proper extensions [12, Problem P6]. We show how to construct many new examples of finite simple relation algebras that have no simple proper extensions, thus providing a partial answer for this second problem. These algebras are also integral and nonrepresentable.? Andréka, Jónsson, Németi [1, Problem 2] (see [12, Problem P7]) asked whether there is a countable simple relation algebra that cannot be embedded in a one-generated relation algebra. The answer is “yes”. Givant [3, Problem 9] asked whether there is some k such that every finitely generated simple relation algebra can be embedded in a k-generated simple relation algebra. The answer is “no”. Received November 27, 1996; accepted in final form July 3, 1997.     

A Note on Collars of Simple Closed Geodesics

For compact hyperbolic Riemann surfaces, the collar theorem gives a lower bound on the distance between a simple closed geodesic and all other simple closed geodesics that do not intersect the initial geodesic. Here it is shown that there are two possible configurations, and in each configuration there is a natural collar width associated to a simple closed geodesic. If one extends the natural collar of a simple closed geodesic α by ε >0, then the extended collar contains an infinity of simple closed geodesics that do not intersect α.Mathematics Subject Classiffications (2000). primary: 30F45; secondary: 32G07     

On Spectra of Almost Simple Extensions of Even-Dimensional Orthogonal Groups

The spectrum of a finite group is the set of the orders of its elements. We consider the problem that arises within the framework of recognition of finite simple groups by spectrum: Determine all finite almost simple groups having the same spectrum as its socle. This problem was solved for all almost simple groups with exception of the case that the socle is a simple even-dimensional orthogonal group over a field of odd characteristic. Here we address this remaining case and determine the almost simple groups in question.Also we prove that there are infinitely many pairwise nonisomorphic finite groups having the same spectrum as the simple 8-dimensional symplectic group over a field of characteristic other than 7.     

Simple Virasoro modules which are locally finite over a positive part

We propose a very general construction of simple Virasoro modules generalizing and including both highest weight and Whittaker modules. This construction enables us to classify all simple Virasoro modules that are locally finite over a positive part. To obtain those irreducible Virasoro modules, we use simple modules over a family of finite dimensional solvable Lie algebras. For one of these algebras, all simple modules are classified by R. Block and we extend this classification to the next member of the family. As a result, we recover many known but also construct a lot of new simple Virasoro modules. We also propose a revision of the setup for study of Whittaker modules.     

Finite simple groups and localization

The purpose of this paper is to explore the concept of localization, which comes from homotopy theory, in the context of finite simple groups. We give an easy criterion for a finite simple group to be a localization of some simple subgroup and we apply it in various cases. Iterating this process allows us to connect many simple groups by a sequence of localizations. We prove that all sporadic simple groups (except possibly the Monster) and several groups of Lie type are connected to alternating groups. The question remains open whether or not there are several connected components within the family of finite simple groups. Partially supported by DGESIC grant PB97-0202 and the Swiss National Science Foundation. Partially supported by the Swiss National Science Foundation.     

Is topologically simple simple?

In this note we determine when topological simplicity of a subsemigroup implies its simplicity. A measure theoretic approach is used. The main result is: In a locally compact completely simple semigroup whose maximal subgroups are compact, every subsemigroup which is either locally compact or of non-empty interior is completely simple. As a corollary, we have: In a compact semigroup, any topologically simple subsemigroup which is either locally compact or of non-empty interior is simple.     

连通简单$r$-一致超图的约化

It is proved in this paper that if G is a simple connected r-uniform hypergraph with G ≥ 2, then G has an edge e such that G-e-V1(e) is also a simple connected r-uniform hypergraph. This reduction is naturally called a combined Graham reduction. Under the simple reductions of single edge removals and single edge contractions, the minor minimal connected simple r-uniform hypergraphs are also determined.     

Computing simple circuits from a set of line segments

We address the problem of connecting line segments to form the boundary of a simple polygon—a simple circuit. However, not every set of segments can be so connected. We present anO(n logn)-time algorithm to determine whether a set of segments, constrained so that each segment has at least one endpoint on the boundary of the convex hull of the segments, admits a simple circuit. Furthermore, this technique can also be used to compute a simple circuit of minimum perimeter, or a simple circuit that bounds the minimum area, with no increase in computational complexity.     

On the Buchstaber Invariant of Simple Convex 3-Polytopes

In this paper the author gives a method of constructing characteristic matrices,and uses it to determine the Buchstaber invariants of all simple convex 3-polytopes,which imply that each simple convex 3-polytope admits a characteristic function.As a further application of the method,the author also gives a simple new proof of five-color theorem.