On analytic analogues of quantum groups

2018/06/27 by Craig Smith, Smith, Craig
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1806.10502

openalex publication_date 2018/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present a new construction of analytic analogues of quantum groups over non-Archimedean fields and construct braided monoidal categories of their representations. We do this by constructing analytic Nichols algebras and use Majid's double-bosonisation construction to glue them together. We then go on to study the rigidity of these analytic quantum groups as algebra deformations of completed enveloping algebras through bounded cohomology. This provides the first steps towards a p-adic Drinfel'd-Kohno Theorem, which should relate this work to Furusho's p-adic Drinfel'd associators. Finally, we adapt these constructions to working over Archimedean fields.

Citations

• The pentagon relation for the quantum dilogarithm and quantized M_0,5
• Quantum groups and representations of monoidal categories
• A Tannakian Reconstruction Theorem for IndBanach Spaces

Related

• Rigid analytic quantum groups and quantum Arens-Michael envelopes
• A Beilinson-Bernstein Theorem for analytic quantum groups
• Quantum groups and representations of monoidal categories
• The analytic structure of an algebraic quantum group
• On Braided Quantum Groups