Exact large ideals of B(G) are downward directed
S. Kaliszewski, Magnus B. Landstad, John Quigg
TL;DR
This paper investigates the properties of large ideals in B(G) related to coaction functors, proving that the intersection of such ideals preserves exactness and providing a counterexample for restrictions to maximal coactions.
Contribution
It establishes that the intersection of large ideals with exact coaction functors remains exact and presents a counterexample regarding restrictions to maximal coactions.
Findings
Intersection of large ideals with exact coaction functors is also exact
Counterexample of a coaction functor not arising from any large ideal when restricted to maximal coactions
Abstract
We prove that if E and F are large ideals of B(G) for which the associated coaction functors are exact, then the same is true for the intersection of E and F. We also give an example of a coaction functor whose restriction to the maximal coactions does not come from any large ideal.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology