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Some Representation Theory of Decorated Partial Brauer Algebra

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

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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)
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

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