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Dissertation
Semigroup approach to representation theory of infinite wreath products
Doctor of Philosophy (Ph.D.), Drexel University
Aug 2010
DOI:
https://doi.org/10.17918/etd-3370
Abstract
We consider the group S(1) of all permutations of the set of naturals, N, with topology of pointwise convergence. Lieberman proved that any representation T of the S(1) is a direct sum of irreducible representations; in particular, T generates a von Neumann algebra of type I. Lieberman's proof is very complicated and can hardly be applied to more general semigroups. Olshanski found another proof of Lieberman's theorem based on semigroup approach. Using this approach we extend the Lieberman's Theorem on the case of the wreath product of S(1) with Z2 endowed with the topology of pointwise convergence.
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Details
- Title
- Semigroup approach to representation theory of infinite wreath products
- Creators
- Yun S. Yoo - DU
- Contributors
- Robert Paul Boyer (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 3370; 991014632275704721