# Bicovariant quantum algebras and quantum Lie algebras

@article{Schupp1992BicovariantQA, title={Bicovariant quantum algebras and quantum Lie algebras}, author={Peter Schupp and Paul Watts and Bruno Zumino}, journal={Communications in Mathematical Physics}, year={1992}, volume={157}, pages={305-329} }

AbstractA bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun
$$(\mathfrak{G}_q )$$
toUqg, given by elements of the pure braid group. These operators—the “reflection matrix”Y≡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…

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