C*-bundle dynamical systems

Abstract

C*-bundle dynamical systems are introduced and their rôle within the theory of C*-subalgebras and Fell bundles is investigated. A C*-bundle dynamical system involves an action of a 1-parameter group of "spatial automorphisms" of the C*-bundle together with a notion of covariance with respect to the diffeomorphisms of the base manifold, and turns out to define a class of examples of Arveson's $A$-dynamical systems. An embedding invariant for non-commutative C*-subalgebras (equivalent to a groupoid 2-cocycle by construction) emerges and has presentation analogous to a partition function towards a potential algebraic formulation of quantum gravity.

27 pages, xypic diagrams. Cross reference to other papers: http://arxiv.org/a/martins_r_2

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Cited by in corpus (2)

• Spectral C*-categories and Fell bundles with path-lifting
• Applications to quantum gravity from C*-bundles