From quantum loop superalgebras to super Yangians

2023/06/13 by Hongda Lin, Yongjie Wang, Lin, Hongda +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2306.07548

openalex publication_date 2023/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to generalize a statement by Drinfeld, asserting that Yangians can be constructed as limit forms of the quantum loop algebras, to the super case. We establish a connection between quantum loop superalgebra and super Yangian of the general linear Lie superalgebra \mathfrakgl_M|N in RTT type presentation. In particular, we derive the Poincaré-Birkhoff-Witt(PBW) theorem for the quantum loop superalgebra U_q(\mathfrakLgl_M|N). Additionally, we investigate the application of the same argument to twisted super Yangian of the ortho-symplectic Lie superalgebra. For this purpose, we introduce the twisted quantum loop superalgebra as a one-sided coideal of U_q(\mathfrakLgl_M|2n) with respect to the comultiplication.

Cited by

• Representations of Quantum Affine General Linear Superalgebras at Arbitrary 01-Sequences
• Drinfeld super Yangian of the exceptional Lie superalgebra D(2,1;λ)

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