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Title: Bosonisations and differentials on inhomogeneous quantum groups
Author: Aziz, Ryan Kasyfil
ISNI:       0000 0004 9348 2060
Awarding Body: Queen Mary University of London
Current Institution: Queen Mary, University of London
Date of Award: 2019
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We dualise Majid's double bosonisation to find a construction of coquasitriangular Hopf Bop > / A . < B* which we call codouble bosonisation, where B is a finite-dimensional braided Hopf algebra living in the category of comodules over coquasitriangular Hopf algebra A. We then construct a reduced quantum coordinate algebra cq[SL2] at q primitive n-th of unity by codouble bosonisation and find new generators for cq[SL2] such that their monomials are essentially a dual basis to the standard PBW basis of the reduced Drinfeld-Jimbo quantum enveloping algebra uq(sl2). Our methods apply in principle for general cq[G] as we illustrate for the case of cq[SL3] at certain odd roots of unity. We also introduce a method of finding differential calculi on double cross product A./H, biproduct A .< B, and bicrossproduct A/H Hopf algebras by constructing their super version. We apply our method to construct the natural differential calculus on the generalised quantum double D(A;H) = Aop./H such that the resulting exterior algebra acts differentiably on H, and on the double coquasitriangular Hopf algebras A./RA such that the resulting exterior algebra acts and coacts differentiably on A. We also construct (Cq[GL2. < C2]) for the quantum group of affine transformation of the plane and (Poinc1;1) for the bicrossproduct Poincaré group in 2 dimensions such that the resulting exterior algebras are strongly bicovariant and coact differentiably on the canonical comodule algebras associated to these inhomogeneous quantum groups.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available