Algebra automorphisms of quantized enveloping algebras \(U_ q({\mathfrak g})\) (Q1337391)

The algebra automorphisms of the quantized enveloping algebras \(U_ q({\mathfrak g})\) are discussed, where \(q\) is generic. Let \(G\) be the group consisting of all deformed algebra automorphisms of \(U_ q({\mathfrak g})\) and \(N\) be its subgroup consisting of all elements which are deformations of the identity automorphisms of \(U({\mathfrak g})\), then \(G/N\) is generated by the following five deformed automorphisms: (i) the Cartan involution, (ii) diagonal automorphisms, (iii) graph automorphisms, (iv) an automorphism \(\delta : \delta(E_ i) = \varepsilon_ i E_ i\), \(\delta(F_ i) = F_ i\), and \(\delta(K_ i) = \varepsilon_ i K_ i\), where \(1 \leq i \leq n\), \(\varepsilon_ i = \pm 1\), (v) the action of the braid group generated by \(T_ i\), which is established by Lusztig.