Azumaya loci of skein algebras

Key Points

• This research aims to compute the azumaya loci of skein algebras, especially focusing on closed surfaces at odd roots of unity.
• Computed azumaya loci for Kauffman-bracket skein algebras of closed surfaces.
• Explored partial results for open surfaces.
• Derived alternative definitions of projective representations of Torelli groups from non-semisimple TQFTs.
• Strengthened existing results regarding dimensions of skein modules of closed 3-manifolds.
• Provided explicit computations of azumaya loci for closed surfaces.
• Offered new definitions that relate to projective representations of Torelli groups.
• Enhanced understanding of dimensions of skein module quotients, building on prior work by Frohman-Kania Bartoszynska-Lê.