Non-semisimple planar algebras from Ūq(sl2)

Moore, Stephen 2016. Non-semisimple planar algebras from Ūq(sl2). PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

We construct examples of non-semisimple tensor categories using planar algebras, with our main focus being on a construction from the restricted quantum group Ūq(sl_2). We describe the generators and prove a number of relations for the Ūq(sl_2) planar algebra, as well as describing diagrammatically various homomorphisms between modules, and conjecture a formula for projections onto indecomposable modules.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Planar Algebras, Restricted Quantum Groups, Quantum Groups, Subfactors, Fusion Categories, Tensor Categories, sl_2, Non-Semisimple, Restricted Quantum sl_2
Funders:	EPSRC
Date of First Compliant Deposit:	23 January 2017
Date of Acceptance:	2 December 2016
Last Modified:	22 Nov 2021 13:59
URI:	https://orca.cardiff.ac.uk/id/eprint/97662

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