Indiana University Mathematics Journal
In recent years both topological and algebraic invariants have been associated to group actions on C*-algebras. Principal bundles have been used to describe the topological structure of the spectrum of crossed products [18, 19], and as a result we now know that crossed products of even the very nicest non-commutative algebras can be substantially more complicated than those of commutative algebras [19, 5]. The algebraic approach involves group cohomological invariants, and exploits the associated machinery to classify group actions on C*-algebras; this originated in , and has been particularly successful for actions of R and tori ([19; Section 4], ). Here we shall look in detail at the relationship between these topological and algebraic invariants, with a view to analyzing the structure of the systems studied in [19; Section 2, 3].
Raeburn, Ian and Williams, Dana P., "Moore Cohomology, Principal Bundles, and Actions of Groups on c*-algebras" (1991). Open Dartmouth: Faculty Open Access Scholarship. 3850.