2018/12/03 by S. Kaliszewski, Kaliszewski, S., Magnus B. Landstad +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L55 #Secondary 46M15
paper · pdf · doi:10.48550/arxiv.1812.01042
openalex publication_date 2018/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a discrete group G, we develop a `G-balanced tensor product' of two coactions (A,δ) and (B,ε), which takes place on a certain subalgebra of the maximal tensor product A⊗max B. Our motivation for this is that we are able to prove that given two actions of G, the dual coaction on the crossed product of the maximal-tensor-product action is isomorphic to the G-balanced tensor product of the dual coactions. In turn, our motivation for this is to give an analogue, for coaction functors, of a crossed-product functor originated by Baum, Guentner, and Willett, and further developed by Buss, Echterhoff, and Willett, that involves tensoring an action with a fixed action (C,γ), then forming the image inside the crossed product of the maximal-tensor-product action. We prove that composing our tensor-product coaction functor with the full crossed product of an action reproduces the tensor-crossed-product functor of Baum, Guentner, and Willett. We prove that every such tensor-product coaction functor is exact, thereby recovering the analogous result for the tensor-crossed-product functors of Baum, Guentner, and Willett. When (C,γ) is the action by translation on ℓ^∞(G), we prove that the associated tensor-product coaction functor is minimal, generalizing the analogous result of Buss, Echterhoff, and Willett for tensor-crossed-product functors.