Bicovariant Quantum Algebras and Quantum Lie Algebras

Details Bicovariant Quantum Algebras and Quantum Lie Algebras Bicovariant Quantum Algebras and Quantum Lie Algebras

1992-10-28

arxiv.org/abs/hep-th/9210150v1

Commun.Math.Phys. 157 (1993) 305-330

Physics

High Energy Physics

High Energy Physics - Theory

38 pages

Scientific paper

10.1007/BF02099762

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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