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Title: The Outer-Temperley-Lieb algebra structure and representation theory
Author: Burke, Heather Maria
Awarding Body: University of Leeds
Current Institution: University of Leeds
Date of Award: 2013
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We define a new algebra the Outer-Temperley-Lieb algebra, OTLn(δ), as a fixed ring of the well known Temperley-Lieb algebra, with respect to an automorphism σ reflecting the known diagrammatic representations of the Temperley-Lieb elements in the vertical plane. We define the cell modules of the Outer-Temperley-Lieb algebra and determine that the algebra’s semi-simplicity is dependant entirely on that of the Temperley-Lieb algebra. We are therefore able to give the complete representation theory of the Outer-Temperley- Lieb algebra when it is semi-simple. The induction and restriction of the standard modules to higher and lower rank OTLn(δ) algebras is studied. We also begin a study of the representation theory of OTLn(δ) when it is not semi-simple by describing a large family of homomorphisms between standard modules and conclude with a conjecture on the labelling set of the blocks of the Outer-Temperley-Lieb algebra in the non semi-simple cases.
Supervisor: Martin, P. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available