Simple Special Jordan Superalgebras with Associative Even Part

We describe the simple special unital Jordan superalgebras with associative even part A whose odd part M is an associative module over A. We prove that each of these superalgebras, not isomorphic to a superalgebra of nondegenerate bilinear superform, is isomorphically embedded into a twisted Jordan superalgebra of vector type. We exhibit a new example of a simple special Jordan superalgebra. We also describe the superalgebras such that M [A,M] 0.     

Structure of some Unital Simple Jordan Superalgebras with Associative Even Part

Studying the unital simple Jordan superalgebras with associative even part, we describe the unital simple Jordan superalgebras such that every pair of even elements induces the zero derivation and every pair of two odd elements induces the zero derivation of the even part. We show that such a superalgebra is either a superalgebra of nondegenerate bilinear form over a field or a four-dimensional simple Jordan superalgebra.     

On Right Alternative Superalgebras

Simple right alternative superalgebras which have a simple algebra as even part and, as odd part, an irreducible bimodule over the even part are investigated. Under these conditions, superalgebras with one dimensional even part are classified, as well as superalgebras having M ₂(F) as even part and a unital irreducible bimodule over M ₂(F) of dimension less than or equal to 6 as odd part. It is shown that there is only a unique non alternative simple right alternative superalgebra of the first type and, for the second type, there is a infinite family depending on a single parameter.     

Alternative Superalgebras with DCC on Two-Sided Ideals#

We study the structure of alternative superalgebras that satisfy the descending chain condition (DCC) for two-sided ideals. The main results state that the Baer radical in an alternative superalgebra of characteristic ≠ 2, 3 with DCC on two-sided ideals is solvable and every such a semiprime superalgebra (of arbitrary characteristic) is isomorphic to a subdirect sum of an associative superalgebra with this property and a finite direct sum of simple alternative non-associative superalgebras.     

Derivations of the Even Part of Finite-Dimensional Simple Modular Lie Superalgebra M

Let F be the underlying base field of characteristic p > 3 and denote by M the even part of the finite-dimensional simple modular Lie superalgebra M. In this paper, the generator sets of the Lie algebra M which will be heavily used to consider the derivation algebra Der(M) are given. Furthermore, the derivation algebra of M is determined by reducing derivations and a torus of M, i.e.,As a result, the derivation algebra of the even part of M does not equal the even part of the derivation superalgebra of M.     

There Exists a Simple Non Trivial t-design with an Arbitrarily Large Automorphism Group for Every t

In 1987, Teirlinckproved that if t and are two integers such that v t(mod(t + 1)!^(2t+1) and v t + 1 >0, then there exists a t - (v, t + 1, (t + 1)!^(2t+1)) design. We prove that if there exists a (t+1)-(v,k,)design and a t-(v-1,k-2, (k-t-1)/(v-k+1))design with t 2, then there exists a t-(v+1,k, (v-t+1)(v-t)/ (v-k+1)(k-t))design. Using this recursive construction, we prove that forany pair (t,n) of integers (t 2and n 0), there exists a simple non trivial t-(v,k,) design having an automorphism groupisomorphic to ⁿ ₂.     

Quasiassociative Algebras with Simple Artinian Null Part

We prove that any quasiassociative algebra with simple Artinian null part is isomorphic to a unique matrix algebra M_n(), where is a quasiassociative division algebra.     

4-Dimensional compact projective planes with a 5-dimensional nilradical

The article is a contribution to the classification of all 4-dimensional flexible compact projective planes. We assume that the collineation group is a 6-dimensional solvable Lie group which fixes some flag. If, moreover, the nilradical of the collineation group is 5-dimensional, then we get 4 families of new planes which are neither translation planes nor shift planes.Meinem Lehrer H. Salzmann zum 65. Geburtstag am 3.11.1995 in Dankbarkeit gewidmet     

Trivial and Simple Spectrum for SL(d,R) Cocycles with Free Base and Fiber Dynamics

Let AC_D(M,SL(d,R))dcnote the pairs(f,A)so that f∈ADiff~1(M)is a C~1-Anosov transitive diffeomorphisms and A is an SL(d,R)cocycle dominated with respect to f.We prove that open and densely in ACd(M,SL(d,R)),in appropriate topologies,the pair(f,A)has simple spectrum with respect to the unique maximal entropy measureμf.Then,we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AutLeb(M)×L~p(M,SL(d,R)).     

Simple Euclidean Arrangements with No (≥ 5)-Gons

It is shown that if a simple Euclidean arrangement of n pseudolines has no (≥ 5)-gons, then it has exactly n - 2 triangles and (n - 2)(n - 3)/2 quadrilaterals. We also describe how to construct all such arrangements, and as a consequence we show that they are all stretchable.     

幂次为2,3,4,5的素变量非线性型的整数部分

考虑了一个混合幂次为2,3,4,5的素变量非线性型的整数部分表示无穷多素数的问题.运用Davenport-Heilbronn方法证明了:如果λ_1,λ_2,λ_3,λ_4是正实数,至少有一个λ_i/λ_j(1≤ij≤4)是无理数,那么存在无穷多素数p_1,p_2,p_3,p_4,p,使得[λ_1p_1~2+λ_2p_2~3+λ_3p_3~4+λ_4p_4~5]=p.