Some Representation Theory of Decorated Partial Brauer Algebra

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.