Morita invariants of quasitriangular comodule algebras

2025/08/27 by Müller, Monique, Walton, Chelsea
#16T05 #18M15 #20F36 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.19845

Abstract

We use representations of braid groups of Coxeter types BC and D to produce invariants of representation categories of quasitriangular comodule algebras. Such categories form a prevalent class of braided module categories. This is analogous to how representations of braid groups of Coxeter type A produce invariants of representation categories of quasitriangular Hopf algebras, a prevalent class of braided monoidal categories. This work also includes concrete examples, and classification results for K-matrices of quasitriangular comodule algebras.

Citations

• Reflective centers of module categories and quantum K-matrices
• Algebraic structures in group-theoretical fusion categories
• Log-modular quantum groups at even roots of unity and the quantum Frobenius I
• Computing Modular Data for Pointed Fusion Categories
• Integrals in left coideal subalgebras and group-like projections
• Braided Morita equivalence for finite-dimensional semisimple and cosemisimple Hopf algebras
• Universal K-matrix for quantum symmetric pairs
• Representations of the category of modules over pointed Hopf algebras over S₃ and S₄
• Polynomial invariants for a semisimple and cosemisimple Hopf algebra of finite dimension
• Monoidal Morita invariants for finite group algebras
• Projectivity and freeness over comodule algebras
• Braid pictures for Artin groups

Related

• Nondegenerate module categories
• The doubles of a braided Hopf algebra
• Monoidal Morita invariants for finite group algebras
• More examples of pseudosymmetric braided categories
• Braided Morita equivalence for finite-dimensional semisimple and cosemisimple Hopf algebras