Higher Spin Algebras and Universal Enveloping Algebras

Abstract

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 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. Show more