The quantum Frobenius for character varieties and multiplicative quiver varieties

Research output: Working paper


We prove that quantized multiplicative quiver varieties and quantum character varieties define sheaves of Azumaya algebras over the corresponding classical moduli spaces, and we prove that the Azumaya locus of the Kauffman bracket skein algebras contains the smooth locus, proving a strong form of the Unicity Conjecture of Bonahon and Wong. The proofs exploit a strong compatibility between quantum Hamiltonian reduction and the quantum Frobenius homomorphism as it arises in each setting. We therefore introduce the concepts of Frobenius quantum moment maps and their Hamiltonian reduction, and of Frobenius Poisson orders. We use these tools to construct canonical central subalgebras of quantum algebras, and explicitly compute the resulting Azumaya loci we encounter, using a natural nondegeneracy assumption.
Original languageEnglish
Number of pages64
Publication statusPublished - 30 Mar 2020


  • 17B37 Quantum groups (quantized enveloping algebras) and related deformations
  • 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)


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