On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups

2024/07/30 by Marco De Renzi, De Renzi, Marco, Jules Martel +1
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Quantum Computing Algorithms and Architecture #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2407.20644

openalex publication_date 2024/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a root of unity ζ of odd prime order, we restrict coefficients of non-semisimple quantum representations of mapping class groups associated with the small quantum group \mathfraku_ζ\mathfraksl₂ from ℚ(ζ) to ℤ[ζ]. We do this by exhibiting explicit bases of states spaces that span ℤ[ζ]-lattices that are invariant under projective actions of mapping class groups.

Related

• Homological Construction of Quantum Representations of Mapping Class Groups
• Revisiting the Steinberg representation at arbitrary roots of 1
• Introduction to quantum representations of mapping class groups
• Rigidity of SU(2) and SO(3) quantum representations of mapping class groups at prime levels
• Irreducibility of some quantum representations of mapping class groups