Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(m|n)]

Details Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(m|n)] Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(m|n)]

2005-04-19

arxiv.org/abs/math/0504373v1

Mathematics

Quantum Algebra

24 pages

Scientific paper

Representations of quantum superalgebras provide a natural framework in which to model supersymmetric quantum systems. Each quantum superalgebra, belonging to the class of quasi-triangular Hopf superalgebras, contains a universal R-matrix which automatically satisfies the Yang--Baxter equation. Applying the vector representation, which acts on the vector module V, to the left-hand side of a universal R-matrix gives a Lax operator. In this Communication a Lax operator is constructed for the quantised orthosymplectic superalgebras U_q[osp(m|n)] for all m > 2, n >\geq 0 where n is even. This can then be used to find a solution to the Yang--Baxter equation acting on V\otimes V\otimes W, where W is an arbitrary U_q[osp(m|n)] module. The case W=V is studied as an example.

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