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arXiv · hep-th/9210150

Bicovariant Quantum Algebras and Quantum Lie Algebras

Peter Schupp·Paul Watts·Bruno Zumino
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Abstract

A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from \fun\ to \uqg\ , given by elements of the pure braid group. These operators --- the `reflection matrix' $Y \equiv L^+ SL^-$ being a special case --- generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for $Y$ in $SO_q(N)$.

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Peter Schupp, Paul Watts, Bruno Zumino. 1992-10-28. Bicovariant Quantum Algebras and Quantum Lie Algebras. https://doi.org/10.1007/bf02099762

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