δ-Jordan李超代数的交换扩张

通过δ-Jordan李超代数T的表示和上同调理论,构造δ-Jordan李超代数T■V.证明了δ-Jordan李超代数的等价交换扩张给出相同的表示.通过δ-Jordan李超代数的表示和其交换扩张得到2-上圈.     

The Yangian double of the Lie superalgebra A(m, n)

The Yangian double DY(A(m, n)) of the Lie superalgebra A(m, n) is described in terms of generators and defining relations. Normally ordered bases in the Yangian and its dual in the quantum double are introduced. We calculate the pairing between the elements of these bases and obtain a formula for the universal R-matrix of the Yangian double as well as a formula for the universal R-matrix (introduced by Drinfeld) of the Yangian.     

A new explicit expression of the Contou-Carrère symbol

The aim of this note is to offer a new explicit expression of the Contou-Carrère symbol that depends only on a product of a finite number of terms. As an application, we obtain an explicit formula for a Witt Residue.

     

素特征域上广义Witt李超代数的自同构群

设W是素特征域上无限维或有限维广义Witt李超代数.本文利用W的自然滤过不变性和W的底代数的不变维数性质,证明了W的自同构群AutW同构于W的底代数的容许自同构群,还证明了在此群同构之下,AutW的标准正规列恰好对应W的底代数的容许自同构群的标准正规列,并给出AutW若干较为细致的性质.     

Witt Groups of Derived Categories

We define the notion of cobordism of two objects in a trianulated category, and the Witt group of such category is defined as the Grothendieck group of cobordism classes of self-dual objects. We prove that the Witt group of a t-category is a free Abelian group generated by the classes of irreducible self-dual objects of its heart. In case of derived category of of complexes of sheaves on a stratified space with the middle-perversity t-structure, these irreducibles are local systems on the strata.     

Graded Witt ring and unramified cohomology

It is proved that for a smooth affine curveX over a local ring or global field, the graded Witt ring ofX is isomorphic to the graded unramified cohomology ring ofX. IfX is projective and has a rational point, the same result holds if and only if every quadratic space defined on the complement of a rational point extends toX. Such an extension is possible, for instance, if the canonical line bundle onX is a square in PicX.     

Hochschild cohomologies and deformations of the pointwise superproduct

We consider the associative superalgebra of smooth compactly supported functions on ℝ ⁿ taking values in a Grassmann algebra. We find the lower Hochschild cohomologies and also the deformations of this superalgebra under certain additional conditions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 323–346, March, 2009.     

一类Weyi型单李超代数

本文研究了单李超代数的构造理论.借助于张量积方法,定义了一类Weyl型结合超代数和一类Weyl型李超代数,并且证明了这类Weyl型结合超代数和Weyl型李超代数是单的充分必要条件.