Quantum Lie algebras associated to $U_q(gl_n)$ and $U_q(sl_n)$

Details Quantum Lie algebras associated to $U_q(gl_n)$ and $U_q(sl_n)$ Quantum Lie algebras associated to $U_q(gl_n)$ and $U_q(sl_n)$

1995-08-22

arxiv.org/abs/q-alg/9508013v1

J.Phys.A29:5611-5618,1996

Physics

High Energy Physics

High Energy Physics - Theory

Latex 9 pages

Scientific paper

10.1088/0305-4470/29/17/031

Quantum Lie algebras $\qlie{g}$ are non-associative algebras which are embedded into the quantized enveloping algebras $U_q(g)$ of Drinfeld and Jimbo in the same way as ordinary Lie algebras are embedded into their enveloping algebras. The quantum Lie product on $\qlie{g}$ is induced by the quantum adjoint action of $U_q(g)$. We construct the quantum Lie algebras associated to $U_q(gl_n)$ and $U_q(sl_n)$. We determine the structure constants and the quantum root systems, which are now functions of the quantum parameter $q$. They exhibit an interesting duality symmetry under $q\leftrightarrow 1/q$.

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