Construction and uniqueness of the C*-Weyl algebra over a general pre-symplectic space
Construction and uniqueness of the C*-Weyl algebra over a general pre-symplectic space
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一般预辛空间上 C*-Weyl 代数的构造和唯一性
DOI：
10.1063/1.1757036
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发表时间：
2004
影响因子：
1.3
通讯作者：
A. Rieckers
中科院分区：
文献类型：
--
作者：
E. Binz;R. Honegger;A. Rieckers
本文以一种几乎自包含的方式，系统地讨论了C*-Weyl代数W（E,σ）在可能无限维的实向量空间E上可能退化的预辛形式σ上的问题。该构造基于对合半群及其相关的射影酉群表示上σ-正定函数的Kolmogorov分解理论。σ-正定函数还提供了W（E,σ）的C*-范数，证明了W（E,σ）与离散向量群E的扭曲群C*-代数是*-同构的，并指出了与相关构造的联系。概述了任意预辛σ的基本对称性的处理。该构造方法特别应用于平凡辛形式σ=0，得到E上的交换Weyl代数，该交换Weyl代数与E的拓扑对偶Eτ′上关于任意局部凸Ha的概周期连续函数的C*-代数同构。
A systematic approach to the C*-Weyl algebra W(E,σ) over a possibly degenerate pre-symplectic form σ on a real vector space E of possibly infinite dimension is elaborated in an almost self-contained manner. The construction is based on the theory of Kolmogorov decompositions for σ-positive-definite functions on involutive semigroups and their associated projective unitary group representations. The σ-positive-definite functions provide also the C*-norm of W(E,σ), the latter being shown to be *-isomorphic to the twisted group C*-algebra of the discrete vector group E. The connections to related constructions are indicated. The treatment of the fundamental symmetries is outlined for arbitrary pre-symplectic σ. The construction method is especially applied to the trivial symplectic form σ=0, leading to the commutative Weyl algebra over E, which is shown to be isomorphic to the C*-algebra of the almost periodic continuous function on the topological dual Eτ′ of E with respect to an arbitrary locally convex Ha...