2023/06/26 by Stukopin, Vladimir, Volkov, Vasiliy
Mathematics · Physics and Astronomy · #17B37 17B67 #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.2306.14598
openalex publication_date 2023/06/26 · openalex created_date 2023/06/28 · openalex updated_date 2026/07/28
We define affine Super Yangian Yℏ(sl(m|n), Π) for affine special linear superalgebra sl(m|n) and arbitrary system of simple roots Π in terms of minimalistic system of generators. We also consider Drinfeld presentation for affine super Yangian in the case of arbitrary simple root system Π and prove that these two presentations (Drinfeld and minimalistic) of Yℏ(sl(m|n), Π) are isomorphic as associative superalgebras. We also construct isomorphism of affine super Yangians Yℏ(sl(m|n), Π) and Yℏ(sl(m|n), Π') for different simple root systems Π and Π'. After them we also define Weyl groupoid as a set of morphisms in category with objects, which are super Yanginas Yℏ(sl(m|n), Π), where Π is simple root system. We describe Weyl groupoid in terms of generators and describe action of these generators on super Yangians. We describe isomorphisms between Yℏ(sl(m|n), Π) and Yℏ(sl(m|n), Π') as elements of Weyl groupoid.