Structure and properties of the algebra of partially transposed permutation operators

Understand

We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term.

• Using purely algebraical methods we show that this algebra is semi-simple and then, considering its regular representation, we derive basic properties of the algebra.
• In particular, we describe all irreducible representations of the algebra of partially transposed operators and derive expressions for matrix elements of the representations.
• It appears that there are two types of irreducible representations of the algebra.