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Title: Universal enveloping algebras of semi-direct products of Lie algebras and their quantum analogues
Author: Lu, Tao
ISNI:       0000 0004 5918 7084
Awarding Body: University of Sheffield
Current Institution: University of Sheffield
Date of Award: 2016
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The thesis consists of two parts. In the first part (Chapters 3 and 4), we study the universal enveloping algebra U(sl2 n V2) of the semi-direct product Lie algebra sl2 n V2 and its subalgebra U(b n V2). In the second part (Chapters 5 and 6), we introduce and study the quantum analogues of these two algebras, i.e, the smash product algebra Kq[X, Y ] o Uq(sl2) and its subalgebra Kq[X, Y ] o U >0 q (sl2). The prime, completely prime, primitive and maximal ideals of these algebras are classified, the generators and inclusions of prime ideals are given explicitly. We also give classifications of all the simple weight modules over the algebras U(sl2 n V2) and Kq[X, Y ] o Uq(sl2). In Chapter 4, a central extension of the Lie algebra sl2 n V2 is also studied, which is called in the literature the Schrödinger algebra. It is conjectured that there is no simple singular Whittaker module for the Schrödinger algebra. We construct a family of such modules. We also proved that the conjecture holds 'generically'.
Supervisor: Bavula, Vladimir ; Jordan, David Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available