Independence of group algebras
Copyright policy )Independence of group algebras
AbstractIt is shown that major independence conditions for left and right group operator algebras coincide. If Σ is a discrete ICC group, then the reduced left and right group algebras W*λ(Σ) and Wϱ*(Σ) are W*‐independent. These algebras are moreover independent in the product sense if, and only if, Σ is amenable. If A and B are subgroups of Σ, then the left and right reduced group (sub)algebras W*λ(A) and Wϱ*(B) are W*‐independent provided that any of the following two conditions is satisfied: (i) A and B have trivial intersection; (ii) A or B is ICC. The results indicate an interplay between intrinsic group‐theoretic properties and independence of the corresponding group algebras that can be further exploited. New examples of W*‐independent von Neumann algebras arising from groups are generated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
- University of Rome Tor Vergata Italy
- University of Chieti-Pescara Italy
- Czech Technical University in Prague Czech Republic
- Sapienza University of Rome Italy
- Chulalongkorn University Thailand
General theory of \(C^*\)-algebras, group algebras, \(C^{*}\)-independence, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, General theory of von Neumann algebras, \(W^{*}\)-independence, C*-independence; Group algebras; W*-independence; Mathematics (all)
General theory of \(C^*\)-algebras, group algebras, \(C^{*}\)-independence, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, General theory of von Neumann algebras, \(W^{*}\)-independence, C*-independence; Group algebras; W*-independence; Mathematics (all)
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