2019/09/30 by Lorenz Eberhardt, Eberhardt, Lorenz, Tomáš Procházka +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1910.00041
openalex publication_date 2019/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a quadratic basis of generators of matrix-extended W1+∞ using a generalization of the Miura transformation. This makes it possible to conjecture a closed-form formula for the operator product expansions defining the algebra. We study truncations of the algebra. An explicit calculation at low levels shows that these are parametrized in a way consistent with the gluing description of the algebra. It is perhaps surprising that in spite of the fact that the algebras are rather complicated and non-linear, the structure of their truncations follows very simple gluing rules.