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Uniform TitleGraded traces and irreducible representations of Aut(A(Gamma)) acting on graded A(Gamma) and A(Gamma)!
NameDuffy, Colleen M. (author), Wilson, Robert (chair), Retakh, Vladimir (internal member), Taft, Earl (internal member), Postnikov, Alexander (outside member), Rutgers University, Graduate School - New Brunswick,
Degree Date2008-05
Date Created2008
SubjectMathematics,
Noncommutative algebras,
Directed graphs
DescriptionIn 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).
NotePh.D.
NoteIncludes bibliographical references (p. 82-83).
Genretheses
Persistent URLhttp://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17304
LanguageEnglish
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.