Deformation of Yangian Y(sl₂)

1995/11/10 by S. Khoroshkin, Khoroshkin, S. M., Alexander Stolin +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.q-alg/9511005

openalex publication_date 1995/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A quantization of a non-standard rational solution of CYBE for sl₂ is given explicitly. We obtain the quantization with the help of a twisting of the usual Yangian Y(sl₂. This quantum object (deformed Yangian Y_η,ξ(sl₂)) is a two-parametric deformation of the universal enveloping algebra U(sl₂[u]) of the positive current algebra sl₂[u]. We consider the pseudotriangular structure on Y_η,ξ(sl₂), the quantum double DY_η,ξ(sl₂) its the universal R-matrix and also the RTT-realization of Y_η,ξ(sl₂).

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