A recently invented way of constructing examples of quasitriangular Hopf algebras (in the sense of V. G. Drinfel’d), called ‘twisting’, is presented. Being applied to the deformations \(U_ h{\mathfrak g}\) of universal enveloping algebras of simple Lie algebras \({\mathfrak g}\), this construction results in a Hopf algebra that can be identified with a multiparameter deformation of the algebra of regular functions \({\mathbb{C}}(G)\) on the corresponding Lie group G. The proof is sketched in the simplest case \(G=GL(n)\). In a number of concluding remarks the author discusses the connection of the presented construction with Manin’s examples of multiparameter deformations of \({\mathbb{C}}(GL(n))\) [Yu. I. Manin, Quantum groups and non-commutative geometry (CRM, Montréal, 1988; Zbl 0724.17006)], with link invariants, and more.
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