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On Rota-Baxter Nijenhuis TD algebra

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TitleInfo
Title
On Rota-Baxter Nijenhuis TD algebra
Name (type = personal)
NamePart (type = family)
Aggarwal
NamePart (type = given)
Monica
NamePart (type = date)
1981-
DisplayForm
Monica Aggarwal
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Guo
NamePart (type = given)
Li
DisplayForm
Li Guo
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Keigher
NamePart (type = given)
William
DisplayForm
William Keigher
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Keys
NamePart (type = given)
Charles David
DisplayForm
Charles David Keys
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Sit
NamePart (type = given)
William Yu
DisplayForm
William Yu Sit
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)
2014
DateOther (qualifier = exact); (type = degree)
2014-05
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
There was a long standing problem of G. C. Rota regarding the classi- fication of all linear operators on associative algebras that satisfy algebraic identities. Initially, only very few of such operators were known, for example, the derivative operator, average operator, difference operator and Rota-Baxter operator. Recently, in a paper by L. Guo, W. Sit and R. Zhang, the authors revisited Rota’s problem by concentrating on two classes of operators; differ- ential type operators and Rota-Baxter type operators. One of the Rota-Baxter type operators they found is the Rota-Baxter Nijenhuis TD (RBNTD) oper- ator which puts together the terms of the well-known Rota-Baxter operator, Nijenhuis operator and Leroux’ TD operator. In this dissertation, we initiate a systematic study of the RBNTD operator, extending the previous works on the Rota-Baxter, Nijenhuis and TD operators. After giving basic properties and examples, we construct free commutative and then free (non-commutative) RBNTD algebras. We then use free RBNTD algebras to obtain an extension of the renowned dendriform algebra with five binary operations.
Subject (authority = RUETD)
Topic
Mathematical Sciences
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_5623
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
v, 85 p.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
Monica Aggarwal
Note
Vita.
Subject (authority = ETD-LCSH)
Topic
Combinatorial analysis
Subject (authority = ETD-LCSH)
Topic
Algebra
Subject
Name (authority = LC-NAF)
NamePart (type = personal)
Rota, Gian-Carlo,--1932-1999--Criticism and interpretation
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/T3VM49JG
Genre (authority = ExL-Esploro)
ETD doctoral
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RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Aggarwal
GivenName
Monica
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2014-04-30 19:25:18
AssociatedEntity
Name
Monica Aggarwal
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
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RULTechMD (ID = TECHNICAL1)
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ETD
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windows xp
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