Independence of Group Algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F10%3A00169190" target="_blank" >RIV/68407700:21230/10:00169190 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Independence of Group Algebras
Original language description
It is shown that major independence conditions for left and right group operator algebras coincide. If Gamma is a discrete ICC group, then the reduced left and right group algebras W-lambda*(F) and W-phi*(Gamma) are W*-independent. These algebras are moreover independent in the product sense if, and only if, r is amenable. If A and B are subgroups of Gamma, then the left and right reduced group (sub)algebrasW(lambda)*(A) and W-phi*(B) are W*-independent provided that any of the following two conditionsis 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F07%2F1051" target="_blank" >GA201/07/1051: Algebraic and measure-theoretic aspects of quantum structures</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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