Generalized free wreath products and their operator algebras
Pierre Fima, Arthur Troupel
Source abstract
Abstract We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima‐Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity, and K‐amenability. We study qualitative properties of the associated von Neumann algebra: factoriality, primeness, and absence of Cartan subalgebra and we give a formula for Connes' ‐invariant. Finally, we give some explicit computations of K‐theory groups for C*‐algebras of generalized free wreath products.
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