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Graded traces and irreducible representations of Aut(A(Gamma)) acting on graded A(Gamma) and A(Gamma)!
Descriptive
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Title
Graded traces and irreducible representations of Aut(A(Gamma)) acting on graded A(Gamma) and A(Gamma)!
Name
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Duffy
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Colleen M.
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Colleen M. Duffy
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author
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Wilson
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Robert
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Advisory Committee
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Robert Wilson
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chair
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Retakh
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Vladimir
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Advisory Committee
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Vladimir Retakh
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internal member
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Taft
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Earl
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Advisory Committee
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Earl Taft
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internal member
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Postnikov
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Alexander
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Advisory Committee
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Alexander Postnikov
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outside member
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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theses
OriginInfo
DateCreated
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2008
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2008-05
Language
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English
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electronic
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text/xml
Extent
vii, 84 pages
Abstract
In this work we will study the structure of algebras A(Gamma) associated to directed, layered graphs. The algebras for which we find a decomposition are the algebras related to
pseudo-roots of noncommutative polynomials and algebras associated to the Hasse graphs of polytopes, to the lattice of subspaces of a
finite-dimensional vector space over a finite field, and to the complete layered graph. We will first find the filtration-preserving automorphism group of these algebras and develop methods of calculating the graded trace of an automorphism acting on the algebra. We will then find the multiplicities of the irreducible representations of Aut(A(Gamma)) acting on the
homogeneous components of A(Gamma) and A(Gamma)^!. The methods developed lead us to consider subalgebras of graded A(Gamma).
pseudo-roots of noncommutative polynomials and algebras associated to the Hasse graphs of polytopes, to the lattice of subspaces of a
finite-dimensional vector space over a finite field, and to the complete layered graph. We will first find the filtration-preserving automorphism group of these algebras and develop methods of calculating the graded trace of an automorphism acting on the algebra. We will then find the multiplicities of the irreducible representations of Aut(A(Gamma)) acting on the
homogeneous components of A(Gamma) and A(Gamma)^!. The methods developed lead us to consider subalgebras of graded A(Gamma).
Note
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Ph.D.
Note
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Includes bibliographical references (p. 82-83).
Subject
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Topic
Mathematics
Subject
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Topic
Noncommutative algebras
Subject
(ID = SUBJ3);
(authority = ETD-LCSH)
Topic
Directed graphs
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Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
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rucore19991600001
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17304
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ETD_917
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NjNbRU
Identifier
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doi:10.7282/T3K074MR
Genre
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ETD doctoral
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The author owns the copyright to this work.
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Copyright protected
Availability
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Open
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Name
Colleen Duffy
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Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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Non-exclusive ETD license
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Author Agreement License
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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.
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