Easy quantum groups

2023/12/19 by Teodor Banica, Banica, Teo
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2312.12368

openalex publication_date 2023/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A closed subgroup G⊂_uU_N⁺ is called easy when its associated Tannakian category C_kl=Hom(u^{⊗ k},u^{⊗ l}) appears from a category of partitions, C=span(D) with D=(D_kl)⊂ P, via the standard implementation of partitions as linear maps. The examples abound, and the main known subgroups G⊂ U_N⁺ are either easy, or not far from being easy. We discuss here the basic theory, examples and known classification results for the easy quantum groups G⊂ U_N⁺, as well as various generalizations of the formalism, known as super-easiness theories, and the unification problem for them.

Related

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