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Higher Spin Algebras and Universal Enveloping Algebras

Han, Bolin

Description

Higher spin algebras, arising from the study of the underlying global symmetries of massless higher-spin particles in physics, have become an interesting area in mathematics since people realised these algebras are deeply related to the theory of minimal representations. A well-studied special one-parameter family hs[ ] is shown to be equivalent to a quotient of the universal enveloping algebra (UEA) of sl2. In this thesis, we review the results on hs[ ] with some modi cations and then...[Show more]

dc.contributor.authorHan, Bolin
dc.date.accessioned2019-10-10T02:55:06Z
dc.date.available2019-10-10T02:55:06Z
dc.identifier.urihttp://hdl.handle.net/1885/173639
dc.description.abstractHigher spin algebras, arising from the study of the underlying global symmetries of massless higher-spin particles in physics, have become an interesting area in mathematics since people realised these algebras are deeply related to the theory of minimal representations. A well-studied special one-parameter family hs[ ] is shown to be equivalent to a quotient of the universal enveloping algebra (UEA) of sl2. In this thesis, we review the results on hs[ ] with some modi cations and then construct new higher spin algebras from the UEA of the semi-direct product sl2 n V2. In addition, we also study the centralisers in the UEA of sl2 n Vm for other values of m in preparation to construct more higher spin algebras.
dc.format.mimetypeapplication/pdf
dc.titleHigher Spin Algebras and Universal Enveloping Algebras
dc.typeThesis (Honours)
local.contributor.supervisorBouwknegt, Peter
local.type.degreeHonours
dc.date.issued2018
local.contributor.affiliationMathematical Sciences Institute, Australian National University
local.identifier.doi10.25911/5d9efb94709a9
dc.date.updated2019-10-10T02:40:47Z
dc.provenanceDeposited by Mathematical Sciences Institute in 2019.
local.mintdoimint
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