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Automorphisms of \(sl(2)\) and dynamical \(r\)-matrices. (English) Zbl 0961.81026

Summary: Two outer automorphisms of the space of infinite-dimensional representations of \(sl(2)\) algebra are considered. The similar constructions for the loop algebras and Yangians are presented. The corresponding linear and quadratic \(R\)-brackets include the dynamical \(r\)-matrices.

MSC:

81R12 Groups and algebras in quantum theory and relations with integrable systems
53D50 Geometric quantization
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References:

[1] Lipatov L. N., JETP Lett. 59 pp 596– (1994)
[2] DOI: 10.1088/0305-4470/27/2/038 · Zbl 0824.70008 · doi:10.1088/0305-4470/27/2/038
[3] DOI: 10.1088/0305-4470/27/20/015 · Zbl 0843.17013 · doi:10.1088/0305-4470/27/20/015
[4] DOI: 10.1063/1.531850 · Zbl 0867.58030 · doi:10.1063/1.531850
[5] DOI: 10.1063/1.531575 · Zbl 0863.58035 · doi:10.1063/1.531575
[6] DOI: 10.1088/0305-4470/29/16/038 · Zbl 0899.58023 · doi:10.1088/0305-4470/29/16/038
[7] DOI: 10.1143/PTPS.118.35 · doi:10.1143/PTPS.118.35
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