Classical limit of quantum Borcherds-Bozec algebras

2020/01/21 by Zhaobing Fan, Seok‐Jin Kang, Fan, Zhaobing +5
Mathematics · #16G20 #17B37 #17B67 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2001.07312

openalex publication_date 2020/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathfrakg be a Borcherds-Bozec algebra, U(\mathfrakg) be its universal enveloping algebra and U_q(\mathfrakg) be the corresponding quantum Borcherds-Bozec algebra. We show that the classical limit of U_q(\mathfrakg) is isomorphic to U(\mathfrakg) as Hopf algebras. Thus U_q(\mathfrakg) can be regarded as a quantum deformation of U(\mathfrakg). We also give explicit formulas for the commutation relations among the generators of U_q(\mathfrakg).

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