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Independence of group algebras
Author(s) -
Conti R.,
Hamhalter J.
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200710038
Subject(s) - mathematics , crossed product , group (periodic table) , von neumann architecture , independence (probability theory) , pure mathematics , intersection (aeronautics) , algebra over a field , quantum mechanics , physics , statistics , engineering , aerospace engineering
It 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 W ϱ * (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 W ϱ * ( 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)