✦ LIBER ✦

Independence of group algebras

✍ Scribed by R. Conti; J. Hamhalter

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 152 KB
Volume: 283
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200710038

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

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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