Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.649567
Title: On multiparameter quantum SLn and quantum skew-symmetric matrices
Author: Dite, Alexis
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2006
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Abstract:
Inspired by an observation in a paper by Dipper and Donkin, we tackle the problem of defining a quantum analogue of SLn in the Multiparameter Quantum Matrices setting when the quantum determinant is not central. We construct a candidate for this algebra in a natural way using the process of Noncommutative Dehomogenisation. We go on to show that the object defined has many appropriate properties for such an analogue and observe that our new algebra can also be obtained via a process known as twisting. Finally we see what our definition means in the particular case of Dipper-Donkin Quantum Matrices and also look at the Standard Quantum Matrices case. In Chapter 3 we move on to study, Quantum Skew-symmetric Matrices. We show that a q-Laplace expansion of q-Pfaffians holds and that the highest-length q-Pfaffian is central. Finally we show that a factor of Quantum Skew-symmetric Matrices is isomorphic to Gq(2,n). Quantum Skew-symmetric Matrices are also mentioned in a 1996 paper by Noumi. In Chapter 4 we recall his definition of the algebra and of q-Pfaffians. These definitions are different to those of Strickland. We show that these contrasting definitions are in fact the same when q is not a root of unity. Using Noumi’s definition we show that another Laplace-type expansion, the natural q-analogue of a classical result, holds for q-Pfaffians.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.649567  DOI: Not available
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