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A coaction d of a locally compact group G on a C*-algebra A is maximal if a certain natural map from A times_d G times_{d hat} G onto A otimes K(L^2(G)) is an isomorphism. All dual coactions on full crossed products by group actions are maximal; a discrete coaction is maximal if and only if A is the full cross-sectional algebra of the corresponding Fell bundle. For every nondegenerate coaction of G on A, there is a maximal coaction of G on an extension of A such that the quotient map induces an isomorphism of the crossed products.
We present a new construction of crossed-product duality for maximal coactions that uses Fischers work on maximalizations. Given a group $G$ and a coaction $(A,delta)$ we define a generalized fixed-point algebra as a certain subalgebra of $M(Artimes_
We give the beginnings of the development of a theory of what we call R-coactions of a locally compact group on a $C^*$-algebra. These are the coactions taking values in the maximal tensor product, as originally proposed by Raeburn. We show that the
The residual finite-dimensionality of a $mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this paradigm to genera
Ge asked the question whether $LF_{infty}$ can be embedded into $LF_2$ as a maximal subfactor. We answer it affirmatively by three different approaches, all containing the same key ingredient: the existence of maximal subgroups with infinite index. W
We study residually finite-dimensional (or RFD) operator algebras which may not be self-adjoint. An operator algebra may be RFD while simultaneously possessing completely isometric representations whose generating C*-algebra is not RFD. This has prov