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On the representation theory of the Fuss-Catalan algebras

Hussein, Ahmed Baqer (2017) On the representation theory of the Fuss-Catalan algebras. PhD thesis, University of Leeds.

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Ahmed Hussein PhD thesis.pdf - Final eThesis - complete (pdf)
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Throughout this thesis, we study the representation theory of the Fuss-Catalan algebras, $FC_{2,n}(a, b)$. We prove that these algebras are cellular and we define their cellular basis. In addition, we prove that they form a tower of recollement, and hence, they are quasi-hereditary. By calculating the Gram determinants of certain cell modules for the Fuss-Catalan algebras, we determine when these algebras are not semisimple. Finally, we end with defining homomorphisms between specified cell modules.

Item Type: Thesis (PhD)
Keywords: Representation theory, diagram algebras, cell modules, Gram determinant.
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Depositing User: Mr Ahmed Hussein
Date Deposited: 18 Aug 2017 11:28
Last Modified: 18 Aug 2017 11:28
URI: http://etheses.whiterose.ac.uk/id/eprint/17949

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