Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]

Details Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)] Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]

2005-06-20

arxiv.org/abs/math/0506387v1

Mathematics

Quantum Algebra

15 pages

Scientific paper

10.1088/1742-5468/2006/06/P06011

Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal $R$-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation $\pi$, which acts on the vector module $V$, to one side of a universal $R$-matrix gives a Lax operator. In this paper a Lax operator is constructed for the $C$-type quantum superalgebras $U_q[osp(2|n)]$. This can in turn be used to find a solution to the Yang-Baxter equation acting on $V \otimes V \otimes W$ where $W$ is an arbitrary $U_q[osp(2|n)]$ module. The case $W=V$ is included here as an example.

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