Title: Structure and properties of the algebra of partially transposed permutation operators

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 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)

Institute for Theoretical Physics, University of Wrocław, 50-204 Wrocław (Poland)

Institute for Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk (Poland)

(Poland)

Publication Date:

OSTI Identifier:

22251021

Resource Type:

Journal Article

Resource Relation:

Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; IRREDUCIBLE REPRESENTATIONS; SPACE; TENSORS