2000/05/15 by S. Khoroshkin, S. M. Khoroshkin, J. Lukierski +2 · 8 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine Lie algebra #Affine transformation #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Cartan matrix #Cellular algebra #Current algebra #Group (periodic table) #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum affine algebra #Quantum group #Quantum mechanics #Superalgebra #hep-th #math.QA
paper · pdf · doi:10.1007/s002200100461
published in Communications in Mathematical Physics 220(3), 537-560 (Springer Science+Business Media) · 22 pages, LaTeX
arxiv created 2000/05/15 · openalex publication_date 2001/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show that the quantum affine algebra Uq(A1(1)) and the quantum affine superalgebra Uq(C(2)(2)) admit a unified description. The difference between them consists in the phase factor which is equal to 1 for Uq(A1(1)) and it is equal to -1 for Uq(C(2)(2)). We present such a description for the actions of the braid group, for the construction of Cartan-Weyl generators and their commutation relations, as well for the extremal projector and the universal R-matrix. We give also a unified description for the 'new realizations' of these algebras together with explicit calculations of corresponding R-matrices.