Independence of group algebras | Zendy

Conti R. | Zendy; Hamhalter J. | Zendy

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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)

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