2019/08/22 by Andrei Neguţ, Neguţ, Andrei · 1 citation
Computer Science · Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1908.08395
openalex publication_date 2019/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
As a quantum affinization, the quantum toroidal algebra is defined in terms of its "left" and "right" halves, which both admit shuffle algebra presentations. In the present paper, we take an orthogonal viewpoint, and give shuffle algebra presentations for the "top" and "bottom" halves instead, starting from the evaluation representation of the quantum affine group and its usual R-matrix. An upshot of this construction is a new topological coproduct on the quantum toroidal algebra which extends the Drinfeld-Jimbo coproduct on the horizontal quantum affine subalgebra.