Heisenberg代数的中心扩张

Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions

We introduce the generalized Heisenberg algebra $\mathcal{H}_n$ and construct realizations of the orthogonal and Lorentz algebras by power series in a semicompletion of $\mathcal{H}_n$. The obtained realizations are given in terms of the generating functions for the Bernoulli numbers. We also introduce an extension of the orthogonal and Lorentz algebras by quantum angles and study realizations of the extended algebras in $\mathcal{H}_n$. Furthermore, we show that by extending the generalized Heisenberg algebra $\mathcal{H}_n$ one can also obtain realizations of the Poincare algebra and its ext…

中心对合代数上的Heisenberg群及其自同构

Heisenberg groups and their automorphisms over algebras with central involution

构造了具有中心对合代数上的海森堡群及其自同构群。以素域上的复四元数群代数为例进行了讨论。它的子空间为每个维数为4或更小的实和复二次空间提供了有限的模型，并构造了这些海森堡群和自同构群的表示模型。一个伪微分算子可以并行处理定义在有限域和实数域上的空间。

相空间的分解与海森堡群的分类

Decomposition of phase space and classification of Heisenberg groups

是否每个允许Heisenberg中心扩张的局部紧阿贝尔群同构于局部紧阿贝尔群与它的Pontryagin对偶的乘积？对于所有具有Heisenberg中心扩张的阿贝尔群的常见类型，包括李群和局部域与Adele的有限笛卡儿积，都得到了肯定的回答.此外，对于这些类型的群，它被发现，同构类的阿贝尔群确定海森堡群同构，从而提供了一个分类的海森堡群。

Projective representations of the inhomogeneous symplectic group: Quantum symmetry origins of the Heisenberg commutation relations

Quantum symmetries that leave invariant physical transition probabilities are described by projective representations of Lie groups. The mathematical theory of projected representations for topologically connected Lie groups is reviewed and applied to the inhomogeneous symplectic group ISp(2n). The projective representations are given in terms of the ordinary unitary representations of the central extension of the group with respect to its first homotopy group direct product with its second cohomology group. The second cohomology group of ISp(2n) is the one dimensional abelian group and the ce…

非对易超空间与超海森堡群

Noncommutative Superspace and Super Heisenberg Group

本文考虑了非对易超空间与超海森堡群的关系。构造了超海森堡群的矩阵表示，并将其应用于弦论中出现的二维变形N=（2，2）超空间.我们还构造了一个玩具模型的非中心扩展的“超级海森堡群”。

海森堡七边形本征问题的伽罗瓦作用

Galois actions on the eigenproblem of the Heisenberg heptagon

本文从有理数场$\mathbb{Q}$的有限扩张的观点，分析了具有最近邻相互作用的XXX模型中磁七边形（即N=7个自旋为1/2的节点的环）的海森堡哈密顿量的本征问题的精确解。我们指出，作为主要的结果，这些扩展的相关算术结构，自然引入一些伽罗瓦量子位。它们是模型的希尔伯特空间的二维子空间，基于它们相对于相关伽罗瓦群对世俗行列式的不可分解因子的作用的独特性质，它们承认量子信息学解释为（假设的）计算机的基本存储单元。这些伽罗瓦量子比特被嵌套在子场的晶格上，子场涉及几个最小的场，用于确定本征态（复海森堡场），谱（实海森堡场）和磁配置的傅里叶变换（基于简单的7次方根的分圆场）。伽罗瓦群的相应格的结构是根据库默尔理论提出的，其物理解释是根据本征态、能量和密度矩阵的适当排列来表示的。