Quantum Lie algebras associated to $U_q(g{l}_n)$ and $U_q(s{l}_n)$

Abstract

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 $U_q(g{l}_n)$ and $U_q(s{l}_n)$. 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 $q\leftrightarrow 1/q$.

Latex 9 pages

References in corpus (4)

• An introduction to non-commutative differential geometry on quantum groups
• Quantum and Braided Lie Algebras
• Conserved charges and soliton solutions in affine Toda theory
• On Quantum Lie Algebras and Quantum Root Systems

Cited by in corpus (4)

• The structure of quantum Lie algebras for the classical series B_l, C_l and D_l
• Representations of the Generalized Lie Algebra sl(2)_q
• Relations in quantized function algebras
• On quantum Jacobi identity