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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.]

MSC:

17B65 Infinite-dimensional Lie (super)algebras
17B37 Quantum groups (quantized enveloping algebras) and related deformations

Citations:

Zbl 0741.00068
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