论文标题
C* - 具有共同行动的操作员代数的开发和产品系统共同c* - 代数
C*-envelopes for operator algebras with a coaction and co-universal C*-algebras for product systems
论文作者
论文摘要
宇宙系统由一个可能由离散组配备的无仪式代数组成。我们介绍了cosystem的C*Envelope的概念；粗略地说，这是最小的c* - 代数宇宙系统，它包含原始元素的完全等距副本。我们表明，宇宙系统的c*envelope始终存在，我们解释了它与通常的c*envelope的关系。然后，我们表明，对于紧凑型的产品系统，在群右LCM右LCM半群上，C*-envelope在Carlsen，Larsen，Sims和Vittadello的意义上是共同的，用于FOCK TENSOR代数，配备了其自然辅助。这产生了共同的c*algebra的存在，从而概括了卡尔森，拉尔森，Sims和Vittadello的先前结果，以及Dor-On和Katsoulis的先前结果。我们还意识到张量代数的c*emevelope是Sehnem引入的倒束束的横截面代数的减少，后者在温和的正态性假设下，我们通过Sehnem的强协调理想的形象来识别Fock代数的商。在另一个应用程序中，我们获得了共同代数的HAO-NG同构定理。
A cosystem consists of a possibly nonselfadoint operator algebra equipped with a coaction by a discrete group. We introduce the concept of C*-envelope for a cosystem; roughly speaking, this is the smallest C*-algebraic cosystem that contains an equivariant completely isometric copy of the original one. We show that the C*-envelope for a cosystem always exists and we explain how it relates to the usual C*-envelope. We then show that for compactly aligned product systems over group-embeddable right LCM semigroups, the C*-envelope is co-universal, in the sense of Carlsen, Larsen, Sims and Vittadello, for the Fock tensor algebra equipped with its natural coaction. This yields the existence of a co-universal C*-algebra, generalizing previous results of Carlsen, Larsen, Sims and Vittadello, and of Dor-On and Katsoulis. We also realize the C*-envelope of the tensor algebra as the reduced cross sectional algebra of a Fell bundle introduced by Sehnem, which, under a mild assumption of normality, we then identify to the quotient of the Fock algebra by the image of Sehnem's strong covariance ideal. In another application, we obtain a reduced Hao-Ng isomorphism theorem for the co-universal algebras.
