Alfadhli, Amani Mohammad
(2018)
*Some Representation Theory of Decorated Partial Brauer Algebra.*
PhD thesis, University of Leeds.

Text
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## Abstract

In this thesis we introduce a new family of finite dimensional diagram algebras over a commutative ring with identity, the decorated partial Brauer algebras. These algebras are unital, associative and have a basis consisting of decorated partial Brauer diagrams which are partial Brauer diagrams with possibly decorated edges and decorated isolated vertices. We show that this algebra is a cellular algebra by applying Theorem of Green and Paget to iterated construction . Subsequently, we give an indexing set for the simple modules. Over a field of characteristic different from 2, we determine when the decorated partial Brauer algebra is quasi-hereditary. Finally, we give a complete description of the restriction rule for the cell modules over C.

Item Type: | Thesis (PhD) |
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Academic Units: | The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |

Depositing User: | Miss Amani Alfadhli |

Date Deposited: | 23 Jul 2018 10:22 |

Last Modified: | 23 Jul 2018 10:22 |

URI: | http://etheses.whiterose.ac.uk/id/eprint/20943 |