QuasiLie Algebras and QuasiDeformations. Algebraic Structures Associated with Twisted Derivations
(2006) Abstract
 This thesis introduces a new deformation scheme for Lie algebras, which we refer to as ?quasideformations? to clearly distinguish it from the classical GrothendieckSchlessinger and Gerstenhaber deformation schemes. The main difference is that quasideformations are not in general categorypreserving, i.e., quasideforming a Lie algebra gives an object in the larger category of ?quasiLie algebras?, a notion which is also introduced in this thesis. The quasideformation scheme can be loosely described as follows: represent a Lie algebra by derivations acting on a commutative, associative algebra with unity and replace these derivations with twisted versions. An algebra structure is then imposed, thus arriving at the quasideformed... (More)
 This thesis introduces a new deformation scheme for Lie algebras, which we refer to as ?quasideformations? to clearly distinguish it from the classical GrothendieckSchlessinger and Gerstenhaber deformation schemes. The main difference is that quasideformations are not in general categorypreserving, i.e., quasideforming a Lie algebra gives an object in the larger category of ?quasiLie algebras?, a notion which is also introduced in this thesis. The quasideformation scheme can be loosely described as follows: represent a Lie algebra by derivations acting on a commutative, associative algebra with unity and replace these derivations with twisted versions. An algebra structure is then imposed, thus arriving at the quasideformed algebra. Therefore the quasideformation takes place on the level of representations: we ?deform? the representation, which is then ?pulledback? to an algebra structure.
The different Chapters of this thesis is concerned with different aspects of this quasideformation scheme, for instance: BurchnallChaundy theory for the qdeformed Heisenberg algebra (Chapter II), the (quasiLie) algebraic structure on the vector space of twisted derivations (Chapter III), deformed Witt, Virasoro and loop algebras (Chapter III and IV), Central extension theory (Chapter III and IV), the Lie algebra sl(2) and some associated quadratic algebras. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/546239
 author
 Larsson, Daniel ^{LU}
 supervisor

 Sergei Silvestrov ^{LU}
 opponent

 Professor Fuchs, Jürgen, Institutionen för ingenjörsvetenskap, fysik och matematik, Karlstad Universitet
 organization
 publishing date
 2006
 type
 Thesis
 publication status
 published
 subject
 keywords
 Talteori, fältteori, algebraisk geometri, algebra, gruppteori, Lie Algebras, QuasiDeformations, Number Theory, field theory, algebraic geometry, group theory, QuasiLie Algebras
 pages
 157 pages
 publisher
 Department of Mathematics, Lund University
 defense location
 Room MH:C, Center for Mathematical Sciences, Sölvegatan 18, Lund Institute of Technology
 defense date
 20060224 13:15:00
 ISBN
 9162867393
 language
 English
 LU publication?
 yes
 id
 8d2ceb6ef0344d0cbf88f916101e3bd0 (old id 546239)
 date added to LUP
 20160404 10:58:10
 date last changed
 20181121 21:01:51
@phdthesis{8d2ceb6ef0344d0cbf88f916101e3bd0, abstract = {This thesis introduces a new deformation scheme for Lie algebras, which we refer to as ?quasideformations? to clearly distinguish it from the classical GrothendieckSchlessinger and Gerstenhaber deformation schemes. The main difference is that quasideformations are not in general categorypreserving, i.e., quasideforming a Lie algebra gives an object in the larger category of ?quasiLie algebras?, a notion which is also introduced in this thesis. The quasideformation scheme can be loosely described as follows: represent a Lie algebra by derivations acting on a commutative, associative algebra with unity and replace these derivations with twisted versions. An algebra structure is then imposed, thus arriving at the quasideformed algebra. Therefore the quasideformation takes place on the level of representations: we ?deform? the representation, which is then ?pulledback? to an algebra structure.<br/><br> <br/><br> The different Chapters of this thesis is concerned with different aspects of this quasideformation scheme, for instance: BurchnallChaundy theory for the qdeformed Heisenberg algebra (Chapter II), the (quasiLie) algebraic structure on the vector space of twisted derivations (Chapter III), deformed Witt, Virasoro and loop algebras (Chapter III and IV), Central extension theory (Chapter III and IV), the Lie algebra sl(2) and some associated quadratic algebras.}, author = {Larsson, Daniel}, isbn = {9162867393}, language = {eng}, publisher = {Department of Mathematics, Lund University}, school = {Lund University}, title = {QuasiLie Algebras and QuasiDeformations. Algebraic Structures Associated with Twisted Derivations}, year = {2006}, }