Ol’shanskiĭ, G. I. Twisted Yangians and infinite-dimensional classical Lie algebras. (English) Zbl 0780.17025 Quantum groups, Proc. Workshops, Euler Int. Math. Inst. Leningrad/USSR 1990, Lect. Notes Math. 1510, 104-119 (1992). For most interesting infinite-dimensional Lie algebras, the enveloping algebra turns out to be a “bad object”. For example, in the representation theory of Kac-Moody Lie algebras the very important quadratic Casimir operator does not belong to the universal enveloping algebra. The latter needs to be replaced by a “good extension” which does contain the important “affiliated” elements. Earlier work by the author has shown that, in the case of \(gl(\infty)\), a “good extension” is closely related to the Yangians \(Y(sl(N))\). In this paper, the author addresses the problem for the classical Lie algebras \(A(2\infty)\), \(A(2\infty+1)\) and \(sp(2\infty)\), and finds a solution involving twisted Yangians.[For the entire collection see Zbl 0741.00068.] Reviewer: N.Backhouse (Liverpool) Cited in 2 ReviewsCited in 18 Documents MSC: 17B65 Infinite-dimensional Lie (super)algebras 17B37 Quantum groups (quantized enveloping algebras) and related deformations Keywords:universal enveloping algebra; twisted polynomial current Lie algebras; infinite-dimensional Lie algebras; twisted Yangians Citations:Zbl 0741.00068 PDFBibTeX XMLCite \textit{G. I. Ol'shanskiĭ}, Lect. Notes Math. 1510, 104--119 (1992; Zbl 0780.17025) Full Text: DOI