A New Light on Nets of C*-Algebras and Their Representations

作者：Ruzzi Giuseppe^*; Vasselli Ezio

来源：Communications in Mathematical Physics, 2012, 312(3): 655-694.

DOI：10.1007/s00220-012-1490-3

The present paper deals with the question of representability of nets of C*-algebras whose underlying poset, indexing the net, is not upward directed. A particular class of nets, called C*-net bundles, is classified in terms of C*-dynamical systems having as group the fundamental group of the poset. Any net of C*-algebras has a canonical morphism into a C*-net bundle, the enveloping net bundle, which generalizes the notion of universal C*-algebra given by Fredenhagen to nonsimply connected posets. This allows a classification of nets; in particular, we call injective those nets such that the canonical morphism is faithful. Injectivity turns out to be equivalent to the existence of faithful representations. We further relate injectivity to a generalized ech cocycle of the net, and this allows us to give examples of nets exhausting the above classification. %26lt;br%26gt;Using these results we have shown, in another paper, that any conformal net over S (1) is injective.

• 出版日期2012-6