Universal actions and representations of locally finite groups on metric spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00505502" target="_blank" >RIV/67985840:_____/19:00505502 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11856-019-1856-8" target="_blank" >http://dx.doi.org/10.1007/s11856-019-1856-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11856-019-1856-8" target="_blank" >10.1007/s11856-019-1856-8</a>

Result language
angličtina
Original language name
Universal actions and representations of locally finite groups on metric spaces
Original language description
We construct a universal action of a countable locally finite group (the Hall group) on a separable metric space by isometries. This single action contains all actions of all countable locally finite groups on all separable metric spaces as subactions. The main ingredient is the amalgamation of actions by isometries. We show that an equivalence class of this universal action is generic. We show that the restriction to locally finite groups in our results is necessary as analogous results do not hold for infinite non-locally finite groups. We discuss the problem also for actions by linear isometries on Banach spaces.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF16-34860L" target="_blank" >GF16-34860L: Logic and Topology in Banach spaces</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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