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Dirac cohomology for Hopf-Hecke algebras
Descriptive
TitleInfo
Title
Dirac cohomology for Hopf-Hecke algebras
Name
(type = personal)
NamePart
(type = family)
Flake
NamePart
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Johannes
NamePart
(type = date)
1987-
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Johannes Flake
Role
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author
Name
(type = personal)
NamePart
(type = family)
Sahi
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Siddhartha
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Siddhartha Sahi
Affiliation
Advisory Committee
Role
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chair
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Lepowsky
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James
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James Lepowsky
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Advisory Committee
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(authority = RULIB)
internal member
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(type = personal)
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(type = family)
Retakh
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(type = given)
Vladimir
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Vladimir Retakh
Affiliation
Advisory Committee
Role
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(authority = RULIB)
internal member
Name
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(type = family)
Ciubotaru
NamePart
(type = given)
Dan
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Dan Ciubotaru
Affiliation
Advisory Committee
Role
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outside member
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Rutgers University
Role
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degree grantor
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School of Graduate Studies
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school
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Text
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theses
OriginInfo
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2018
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2018-10
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2018
Place
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xx
Language
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eng
Abstract
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In this dissertation, a generalized version of Dirac cohomology is developed.
It is shown that Dirac operators can be defined and their cohomology can be studied for a general class of algebras, which we call Hopf--Hecke algebras. A result relating the Dirac cohomology with central characters is established for a subclass of algebras, which we call Barbasch--Sahi algebras. This result simultaneously generalizes known results on such a relation for real reductive Lie groups and for various kinds of Hecke algebras, which all go back to a conjecture of David Vogan (1997).
A variety of algebraic concepts and techniques is combined to create the general framework for Dirac cohomology, including central simple (super)algebras, Hopf algebras, smash products, PBW deformations, and Koszul algebras.
Classification results on the studied classes of algebras are obtained, and infinitesimal Cherednik algebras of the general linear group are studied as novel examples for algebras with a Dirac cohomology theory.
It is shown that Dirac operators can be defined and their cohomology can be studied for a general class of algebras, which we call Hopf--Hecke algebras. A result relating the Dirac cohomology with central characters is established for a subclass of algebras, which we call Barbasch--Sahi algebras. This result simultaneously generalizes known results on such a relation for real reductive Lie groups and for various kinds of Hecke algebras, which all go back to a conjecture of David Vogan (1997).
A variety of algebraic concepts and techniques is combined to create the general framework for Dirac cohomology, including central simple (super)algebras, Hopf algebras, smash products, PBW deformations, and Koszul algebras.
Classification results on the studied classes of algebras are obtained, and infinitesimal Cherednik algebras of the general linear group are studied as novel examples for algebras with a Dirac cohomology theory.
Subject
(authority = RUETD)
Topic
Mathematics
Subject
(authority = ETD-LCSH)
Topic
Hecke algebras
Subject
(authority = ETD-LCSH)
Topic
Hopf algebras
Subject
(authority = ETD-LCSH)
Topic
Cohomology operations
RelatedItem
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Title
Rutgers University Electronic Theses and Dissertations
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ETD
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ETD_9215
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (118 pages) : illustrations
Note
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Ph.D.
Note
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Includes bibliographical references
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Title
School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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NjNbRU
Identifier
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doi:10.7282/t3-ss9m-we37
Genre
(authority = ExL-Esploro)
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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Flake
GivenName
Johannes
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Permission or license
DateTime
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2018-09-20 23:43:53
AssociatedEntity
Name
Johannes Flake
Role
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Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
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License
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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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2018-09-20T17:41:45
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2018-09-20T17:41:45
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