因子Von Neumann代数中套子代数上的局部3-上循环

证明了因子von Neumann代数中的套子代数到其单位对偶双模内的每个弱连续的局部3-上循环都是3-上循环.     

2- 上循环交叉积

利用 von Neumann 代数 M 和带有正规的2- 上循环 μ 的离散群 G, 定义了2- 上循环交叉积, 推广了经典的离散交叉积, 并证明了2- 上循环交叉积具有结合律.     

Notes on 2-parameter quantum groupsⅠ

A simpler definition for a class of 2-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form.Their positive parts turn out to be 2-cocycle deformations of each other under some conditions.An operator realization of the positive part is given.     

局部2-上循环

The aim of this paper is to show that every local 2-cocycle of a von Neumann algebra R with coefficients in .Y (a unital dual R-bimodule) is a 2-cocycle.     

三角矩阵上的Hochschild 2-循环广义若当导子

In this paper,we prove that every generalized Jordan derivation associate with a Hochschild 2-cocycle from the algebra of upper triangular matrices to its bimodule is the sum of a generalized derivation and an antiderivation.     

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.     

Notes on 2-parameter quantum groups I

A simpler definition for a class of 2-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An operator realization of the positive part is given. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10431040, 10728102), the TRAPOYT, the FUDP and the Priority Academic Discipline from the MOE of China, the SRSTP from the STCSM, the Shanghai Priority Academic Discipline from the SMEC     

Cocycle d'Euler etK2

In this paper we construct a canonical 2-cocycle on the groupP SL(2,k) with values in the Witt groupW(k) of the fieldk. This allows us to produce anatural homomorphism :H ₂(SL(2,k); Z)I ²(k), whereI ²(k) is the square of the fundamental ideal. We prove that this homomorphism is in fact a lift of Milnor's symbol.

     

Skew pairing, Cocycle deformations and double crossproducts

In this paper, we give a sufficient condition for double crossproductX ⋈A to beX ⋈ _τ A for some skew pairingτ ifX ⋈A is a 2-cocycle deformation ofX ⊗A. Then we give a sufficient and necessary condition forX ⋈A to beX ⋈ _τ A by using natural isomorphism terminology. Supported by Chinese Natural Science Fund     

Properties of Higher-Dimensional Shintani Generating Functions and Cocycles on Pgl3(Q)

In an earlier paper the second author used the formal, algebraicproperties of 2-dimensional Shintani generating functions toconstruct a 1-cocycle on PGL₂{Q}. We aim to generalise theseresults by using such functions in dimension n to obtain an(n–1)-cocycle on PGL_n{Q}, presumably related to the Bernoulliand Eisenstein cocycles of R. Sczech. By improving our methodswe achieve this goal for n=3. For n>3 we encounter obstaclesrelated to degenerate configurations of hyperplanes in n-space.Nevertheless, we obtain partial results closely connected toreciprocity laws for certain n-dimensional Dedekind sums. 1991Mathematics Subject Classification: 11F20, 11F75.     

Nonabelian 1-cohomologies and conjugacy of finite subgroups in some extensions

We describe the conjugacy classes of finite subgroups in some split extensions using the notion of 1-cocycle and 1-coboundary with values in a noncommutative group. We prove that each finite subgroup in the automorphism group of a free Lie algebra of rank 3 is conjugated with a subgroup of the linear automorphism group provided that the group order does not divide the characteristic of the ground field.     

Sur une Question (Orale) de Michèle Vergne

Résumé

On donne une réponse explicite à la question suivante: étant donné un 3-cocycle Φ (sur le groupe G = ? ^N , à valeurs dans le G-module trivial ?) dont l'antisymétrisé est nul, construire une 2-cochaîne admettant Φ comme cobord.

Abstract

We give an explicit answer to the following question: given a 3-cocycle Φ (on the group G = ? ^N , with values in the trivial G-module ?) whose antisymmetric part is zero, construct a 2-cochain having Φ as coboundary.     

Twisted bounded-dilation group C*-algebras as C*-metric algebras

We construct a class of C~*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[M?, ·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C~*-algebra C*r(Γ, σ) for the pointwise multiplication operator M?on ?2(Γ), induced by a proper length function ? on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.     

Effective lifting of 2-cocycles for Galois cohomology

We give explicit formulas for reducing the problem of determining whether a given 2-cocycle is a coboundary and if so finding a lifting 1-cochain to a system of norm equations.     

Trace Invariant and Cyclic Cohomology of Twisted Group C*-Algebras

By the method of cyclic cohomology we prove that all tracial states on a twisted group C*(G;σ), where G is a torsion free discrete group of polynomial growth and σ is a 2-cocycle on G with values in the unit circle group, induce the same map from K₀(C*(G;σ)) into .     

Bijective 1-Cocycles and Classification of 3-Dimensional Left-Symmetric Algebras

Left-symmetric algebras have close relations with many important fields in mathematics and mathematical physics. Their classification is very complicated due to the nonassociativity. In this article, we re-study the correspondence between left-symmetric algebras and the bijective 1-cocycles. Then a procedure is provided to classify left-symmetric algebras in terms of classification of equivalent classes of bijective 1-cocycles. As an example, the 3-dimensional complex left-symmetric algebras are classified.     

Quandle homotopy invariants of knotted surfaces

Given a finite quandle, we introduce a quandle homotopy invariant of knotted surfaces in the 4-sphere, modifying that of classical links. This invariant is valued in the third homotopy group of the quandle space, and is universal among the (generalized) quandle cocycle invariants. We compute the second and third homotopy groups, with respect to “regular Alexander quandles”. As a corollary, any quandle cocycle invariant using the dihedral quandle of prime order is a scalar multiple of Mochizuki 3-cocycle invariant. As another result, we determine the third quandle homology group of the dihedral quandle of odd order.     

Continuous cocycles on locally compact groups: II

In this second paper we continue our development of elementary methods for computing continuous complex-valued solutions of the 2-cocycle functional equation on locally compact groups. The first paper dealt primarily with solvable groups. Here we consider some classical motion groups of mathematical physics, including the Euclidean, Galilean, Lorentz and Poincaré groups.     

Central extensions of some Lie algebras

We consider three Lie algebras: , the Lie algebra of all derivations on the algebra of formal Laurent series; the Lie algebra of all differential operators on ; and the Lie algebra of all differential operators on We prove that each of these Lie algebras has an essentially unique nontrivial central extension.