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Generalized Quasi Poisson structures and noncommutative integrable systems
Descriptive
TitleInfo
Title
Generalized Quasi Poisson structures and noncommutative integrable systems
Name
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Artamonov
NamePart
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Semen
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Semen Artamonov
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author
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Retakh
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Vladimir
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Vladimir Retakh
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chair
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Sahi
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Siddhartha
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Siddhartha Sahi
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Advisory Committee
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internal member
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Weibel
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Charles
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Charles Weibel
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Advisory Committee
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internal member
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Gekhtman
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Michael
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Michael Gekhtman
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Advisory Committee
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outside member
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Rutgers University
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degree grantor
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School of Graduate Studies
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Text
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theses
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2018
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2018-05
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2018
Place
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xx
Language
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eng
Abstract
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The dissertation is devoted to the applications of the Noncommutative Geometry Program to the study of Integrable Systems and Cluster Algebras. In particular, it is shown that cluster algebras introduced by A.~Goncharov and R.~Kenyon admit a noncommutative generalization. This generalization can be viewed as a family of categories equipped with a double Quasi Poisson bracket and a family of functors between these categories which preserve the double bracket. From this perspective, the commutative cluster algebra appears as the coordinate ring of the moduli space of one dimensional representations of the noncommutative cluster algebra. It is shown that Noncommutative systems of ODEs, suggested earlier by M.~Kontsevich and A.~Usnich, admit a formulation as Noncommutative Hamilton flows. Finally, a non-skew-symmetric generalization of the double Poisson bracket is considered. It is shown that such modified double Poisson brackets inherit major properties of double Poisson brackets.
Subject
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Topic
Mathematics
Subject
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Topic
Poisson algebras
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Rutgers University Electronic Theses and Dissertations
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ETD_8798
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electronic resource
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Extent
1 online resource (vii, 75 p. : ill.)
Note
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Ph.D.
Note
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Includes bibliographical references
Note
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by Semen Artamonov
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School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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Identifier
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doi:10.7282/T3125X22
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ETD doctoral
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Rights
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The author owns the copyright to this work.
RightsHolder
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Name
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Artamonov
GivenName
Semen
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Permission or license
DateTime
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2018-04-12 09:35:19
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Semen Artamonov
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Affiliation
Rutgers University. School of Graduate Studies
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Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
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Copyright protected
Availability
Status
Open
Reason
Permission or license
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2018-04-12T00:27:24
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2018-04-12T00:27:24
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