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.

（Co）Homology and Universal Central Extension of Hom-Leibniz Algebras

Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz algebras based on some works of Loday and Pirashvili.

Central extensions of generalized orthosymplectic Lie superalgebras

We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm 12n（R,-） that is coordinatized by an arbitrary unital associative superalgebra （R,-） with superinvolution. As a result, an identification between the second homology group of the Lie superalgebra ospm｜2n （R,-） and the first skew-dihedral homology group of the associative superalgebra （R,-） with superin-volution is created for positive integers m and n with （m, n）≠ （1, 1） and （m, n）≠（2, 1）. The second homology groups of the Lie superalgebras ospm1｜2（R,-） and ospm｜2n （R,-） are also characterized explicitly.

吉林红旗岭晚三叠世镁铁超镁铁质侵入体矿物化学和岩石地球化学特征:对镍铜成矿的启示

吉林红旗岭镁铁超镁铁质侵入岩群位于中亚造山带东段南缘,由3个北西向岩带(I、II、III)组成,包括30多个小岩株,其中I-岩带的部分岩体伴有铜镍矿化,并且其1和7号岩体分别形成了中型和大型岩浆铜镍硫化物型矿床。矿床主要容矿岩石为辉橄岩、橄辉岩、斜方辉石岩、二辉石岩、苏长岩和辉长岩。主量元素方面,红旗岭岩群具有富镁(w(MgO)=20.7%~31.1%)、低钛(w(TiO_(2))=0.33%~0.79%)、低碱(w(K 2 O+Na 2 O)=0.60%~2.29%)和硅(w(SiO_(2))=40.0%~53.0%)变化范围大的特征;微量元素方面,红旗岭岩群呈现弱富集LREE和LILE(Th)以及亏损HREE和HFSE(Nb-Ta-Ti)。岩相学、地球化学和矿物(橄榄石、斜方辉石、单斜辉石、尖晶石、斜长石和角闪石)主微量元素特征表明,红旗岭岩群明显不同于洋岛型玄武岩、阿拉斯加型环状杂岩和科马提岩,但与岛弧玄武岩以及中亚造山带西段的“黄山西”和“黄山东”铜镍硫化物矿床的容矿超镁铁质岩相似,其母岩浆是一种富Mg、亏损Nb-Ta的岛弧拉斑玄武质熔体,形成于晚三叠世古亚洲洋闭合后伸展环境,演化过程中经历了地壳混染和分离结晶作用,含矿母岩浆可能经历了硫化物的“二次熔离”,最终形成了铂族元素(PGE)亏损型岩浆铜镍硫化物矿床。

DERIVATIONS AND EXTENSIONS OF LIE COLOR ALGEBRA

In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.

中南祁连西缘肃北三个洼塘地区古生代两类花岗质侵入岩年代学及其地质意义

中南祁连西缘三个洼塘附近花岗质岩石由花岗岩、石英闪长岩和花岗闪长岩构成。LA—ICP-MS锆石U-Pb年龄测定结果表明，花岗岩、石英闪长岩和花岗闪长岩侵位年龄分别为416．7±4．3Ma（MSWD=0．52）、442．5±4．7Ma（MSWD=0．46）和443．9±1．3Ma（MSWD=0．17），指示本区发生了两期岩浆活动事件。花岗质岩石均表现为过铝质，花岗岩高钾、K／Na，低Mg、Fe、Ca的主量元素特征，富集高场强元素，亏损大离子亲石元素，∑REE为122．0×10^-6，δEu为0．05，具明显负铕异常。花岗闪长岩和石英闪长岩多数富钠，高场强元素含量相对花岗岩较低，而大离子亲石元素含量相对花岗岩略高，∑REE为133．3×10～～247．6×10^-6，δEu为0．73～1．09，铕异常特征不明显。综合研究表明，本区花岗岩可能属于造山活动结束后伸展环境下地壳物质部分熔融形成的A型花岗岩，花岗闪长岩和石英闪长岩则可能属于洋壳俯冲环境下引起岛弧岩浆活动而形成的I型花岗岩，这一成果对于研究中南祁连的构造演化有着重要意义。

冀中坳陷古近纪的伸展构造

冀中坳陷的构造格架是新生代的伸展构造系统。该系统以大兴、保定—石家庄拆离滑脱断层为主体,与牛东—河东、马西、宁晋、新河等伸展断层以及徐水—安新变换带和衡水、宝坻—桐柏镇变换断层等组合而成。据平衡剖面和基底沉降曲线分析,冀中坳陷古近纪伸展作用过程持续发育,具幕式特点,以沙三期伸展作用最为强烈。地壳的快速伸展作用与火山活动强度之间缺乏耦合关系。冀中坳陷的动力学成因与伸展背景下的剪切作用有关。

A special fermionic generalization of lineal gravity

The central extension of the (1+1)-dimensional Poincaré algebra by including fermionic charges which obey not supersymmetric algebra, but a special graded algebra containing in the right hand side a central element only is obtained. The corresponding theory being the fermionic extension of the lineal gravity is proposed. We considered the algebra of generators, the field transformations and found Lagrangian and equation of motion, then we derived the Casimir operator and obtained the con- stant black hole mass.

锡矿山锑矿床成因新解──论伸展构造对超大型锑成矿的控制作用

锡矿山锑矿床的成因众说纷纭，笔者通过对矿区和区域构造的研究，并结合矿床的地球化学特征，发现该矿床是在伸展体制（时代从白垩纪至老第三纪）下由地下热液循环而形成的低温热液矿床，矿区的主要断裂对该矿床的形成具极其重要的控制作用。在此基础上，提出了锡矿山锑矿床一个新的成因模式。

Genetic model of hanging wall syncline and central dome in extensional fault

Hanging wall syncline and central dome are special extension structures, developing over the hanging wall in an extensional ramp-flat fault. Under the condition that the flat is sub-horizontal, the hanging wall syncline is separated from the half graben by the central dome. And on the dome forms an erosional surface. Both sediments in the half graben and erosional surface on the top of the central dome extended over the dome and entered into the hanging wall syncline with extension going on. Meanwhile, those having entered were overlapped by new sedimentary layers in the hanging wall syncline, so that there is a together-threaded, diachronic unconformity to form in the same epoch stratum. The layers in the hanging wall syncline also have an attribute of migrating laterally and getting tilted with extension. There is no sedimentation on the central dome. But sediments, which came from the half graben, got thicker over the dome in extension.

The unitary subgroups of group algebras for a class of finite 2-groups with the derived subgroup of order 2

Let p be a prime and F be a finite field of characteristic p.Suppose that FG is the group algebra of the finite p-group G over the field F.Let V(FG)denote the group of normalized units in FG and let V_(*)(FG)denote the unitary subgroup of V(FG).If p is odd,then the order of V_(*)(FG)is|F|^((|G-1)/2).However,the case p=2 still is open.In this paper,the order of V*(FG)is computed when G is a nonabelian 2-group given by a central extension of the form 1→Z_(2^(n))×Z_(2^(m))→G→Z_(2)×…×Z_(2)→1 and G'≌Z_(2),n,m≥1.Furthermore,a conjecture is confirmed,i.e.,the order of V_(*)(FG)can be divisible by|F|^(1/2(|G|+|Ω1(G)|)-1),where Ω_(1)(G)={g∈G|g^(2)=1}.

Finite 2-groups whose nonnormal subgroups have orders at most 2^3

In this paper, we classify finite 2-groups all of whose nonnormal subgroups have orders at most 2^3. Together with a known result, we completely solved Problem 2279 proposed by Y. Berkovich and Z. Janko in Groups of Prime Power Order, Vol. 3.

Automorphism Groups of Some Finite p-Groups

The automorphism group of G is determined, where G is a nonabelian p-group given by a central extension as 1→Zpm→G→Zp×…×Zp→1 such that its derived subgroup has order p.

Automorphisms and Verma Modules for Generalized 2-dim Affine-Virasoro Algebra

We study the structure of the generalized 2-dim affine-Virasoro algebra, and describe its automorphism group. Furthermore, we also determine the irreducibility of a Verma module over the generalized 2-dim affine-Virasoro algebra.

q-Deformation of W (2 , 2) Lie Algebra Associated with Quantum Groups

The q-deformation of W（2, 2） Lie algebra is well defined based on a realization of this Lie algebra by using the famous bosonic and fermionic oscillators in physics. Furthermore, the quantum group structures on the q-deformation of W（2, 2） Lie algebra are completely determined. Finally, the 1-dimensional central extension of the q-deformed W（2, 2） Lie algebra is studied, which turns out to be coincided with the conventional W（2, 2） Lie algebra in the q → 1 limit.

Twisted toroidal Lie algebras and Moody-Rao-Yokonuma presentation

Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g with respect toμ,which provides a Moody-Rao-Yokonuma presentation for the algebraˆg[μ]whenμis non-transitive,and the presentation is indeed related to the quantization of twisted toroidal Lie algebras.

Hom-Malcev superalgebras

Hom-Malcev superalgebras can be considered as a deformation of Malcev superalgebras. We give the definition of Hom-Malcev superalgebras. Moreover, we characterize the Hom-Malcev operator and the representation of Hom-Malcev superalgebras. Finally, we study the central extension and the double extension of Hom-Malcev superalgebras.

The Structures for the Loop-Witt Algebra

The loop-Witt algebra is the Lie algebra of the tensor product of the Witt algebra and the Laurent polynomial algebra. In this paper we study the universal central extension, derivations and automorphism group for the loop-Witt algebra.

On the Toroidal Leibniz Algebras

Toroidal Leibniz algebras are the universal central extensions of the iterated loop algebras g×C[t1^±1,...,tv^±1] in the category of Leibniz algebras. In this paper, some properties and representations of toroidal Leibniz algebras are studied. Some general theories of central extensions of Leibniz algebras are also obtained.

Finite 2-Groups Whose Number of Subgroups of Each Order are at Most 2^(4)

Assume G is a group of order 2^(n),n≥5.Let s_(k)(G)denote the number of subgroups of order 2^(k) of G.We classify finite 2-groups G with s k(G)≤2^(4),where 1≤k≤n.