RUcore: Rutgers University Community Repository
Algebraic studies of symmetric operators
Descriptive
TitleInfo
Title
Algebraic studies of symmetric operators
Name
(type = personal)
NamePart
(type = family)
Shi
NamePart
(type = given)
Zhiqin
NamePart
(type = date)
1985-
DisplayForm
Zhiqin Shi
Role
RoleTerm
(authority = RULIB)
author
Name
(type = personal)
NamePart
(type = family)
Keigher
NamePart
(type = given)
William
DisplayForm
William Keigher
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
chair
Name
(type = personal)
NamePart
(type = family)
Guo
NamePart
(type = given)
Li
DisplayForm
Li Guo
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Sczech
NamePart
(type = given)
Robert
DisplayForm
Robert Sczech
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Cassidy
NamePart
(type = given)
Phyllis Joan
DisplayForm
Phyllis Joan Cassidy
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
outside member
Name
(type = corporate)
NamePart
Rutgers University
Role
RoleTerm
(authority = RULIB)
degree grantor
Name
(type = corporate)
NamePart
Graduate School - Newark
Role
RoleTerm
(authority = RULIB)
school
TypeOfResource
Text
Genre
(authority = marcgt)
theses
OriginInfo
DateCreated
(qualifier = exact)
2015
DateOther
(qualifier = exact);
(type = degree)
2015-05
CopyrightDate
(encoding = w3cdtf);
(qualifier = exact)
2015
Place
PlaceTerm
(type = code)
xx
Language
LanguageTerm
(authority = ISO639-2b);
(type = code)
eng
Abstract
(type = abstract)
There was an old problem of G. C. Rota regarding the classification of all linear operators on associative algebras that satisfy algebraic identities. We only know very few of such operators at the beginning, for example, the derivative operator, average operator, difference operator and Rota-Baxter operator. Recently L. Guo, W. Sit and R. Zhang revisited Rota's problem in a paper by concentrating on two classes of operators: differential type operators and Rota-Baxter type operators. One of the Rota-Baxter type operators they found is the symmetric Rota-Baxter operator which symmetrizes the Rota-Baxter operator. In this dissertation, we initiate a systematic study of the symmetric Rota-Baxter operator, extending the previous works on the original Rota-Baxter operator. After giving basic properties and examples, we construct free symmetric Rota-Baxter algebras on an algebra and on a set by bracketed words and rooted trees separately. We then use the free symmetric Rota-Baxter algebra to obtain an extension of the well known dendriform algebra and its free objects. Finally, we extend our study to differential algebras. We construct the free symmetric differential Rota-Baxter algebra based on the previous free symmetric Rota-Baxter algebra on a set and the free symmetric differential algebra.
Subject
(authority = RUETD)
Topic
Mathematical Sciences
RelatedItem
(type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
(type = RULIB)
ETD
Identifier
ETD_6467
PhysicalDescription
Form
(authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (vii, 115 p. : ill.)
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Subject
(authority = ETD-LCSH)
Topic
Symmetric operators
Note
(type = statement of responsibility)
by Zhiqin Shi
RelatedItem
(type = host)
TitleInfo
Title
Graduate School - Newark Electronic Theses and Dissertations
Identifier
(type = local)
rucore10002600001
Location
PhysicalLocation
(authority = marcorg);
(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T3RR214G
Genre
(authority = ExL-Esploro)
ETD doctoral
Back to the top
Rights
RightsDeclaration
(ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder
(type = personal)
Name
FamilyName
Shi
GivenName
Zhiqin
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
(encoding = w3cdtf);
(qualifier = exact);
(point = start)
2015-04-30 21:35:37
AssociatedEntity
Name
Zhiqin Shi
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - Newark
AssociatedObject
Type
License
Name
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
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
Back to the top
Technical
RULTechMD
(ID = TECHNICAL1)
ContentModel
ETD
OperatingSystem
(VERSION = 5.1)
windows xp
Back to the top
Statistical Profile