University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Structure and properties of the algebra of partially transposed operators

Structure and properties of the algebra of partially transposed operators

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Mathematical Challenges in Quantum Information

We consider the structure of algebra of n-fold tensor product operators, 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 transformed operators. It appears that there are two kinds of irreducible representations of the algebra. The first one is strictly connected with the representations of the group S(n-1) induced by irreducible representations of the group S(n-2). The second kind is structurally connected with irreducible representations of the group S(n-1).

This talk is part of the Isaac Newton Institute Seminar Series series.

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