论文标题
来自c*-ergebras的小组动作的非共同数值主捆
Noncommutative numerable principal bundles from group actions on C*-algebras
论文作者
论文摘要
我们介绍了本地琐碎的$ g $ -c*-clgebra的定义，该定义是本地紧凑的Hausdorff Numbul numbled principal $ g $ bundle的总空间的非交换性对应物。为了获得这种概括，我们必须超越Gelfand-Naimark二元性，并使用Pedersen理想的乘数。我们的新概念使我们能够调查非交通性主捆绑包的本地琐事，这些捆绑包在非空军C*-代数上采取的小组动作，我们通过来自$ C_0（y）$ - 代数和图形C*-ergebras的示例来说明这一点。在紧凑的Hausdorff群体对Unital C*代数的作用的情况下，在我们的意义上，局部琐碎是由动作局部繁琐维度的有限性暗示的。此外，我们证明，如果$ a $是本地琐碎的$ g $ -c*-c*-algebra，那么$ a $上的$ g $ action在某些意义上是免费的，在许多情况下，这与因Rieffel和Ellwood而引起的已知FreeNess概念恰逢其物。
We introduce a definition of the locally trivial $G$-C*-algebra, which is a noncommutative counterpart of the total space of a locally compact Hausdorff numerable principal $G$-bundle. To obtain this generalization, we have to go beyond the Gelfand-Naimark duality and use the multipliers of the Pedersen ideal. Our new concept enables us to investigate local triviality of noncommutative principal bundles coming from group actions on non-unital C*-algebras, which we illustrate through examples coming from $C_0(Y)$-algebras and graph C*-algebras. In the case of an action of a compact Hausdorff group on a unital C*-algebra, local triviality in our sense is implied by the finiteness of the local-triviality dimension of the action. Furthermore, we prove that if $A$ is a locally trivial $G$-C*-algebra, then the $G$-action on $A$ is free in a certain sense, which in many cases coincides with the known notions of freeness due to Rieffel and Ellwood.
