Classical shadows of stated skein representations at roots of unity

Abstract

We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove that the stated skein algebra with deforming parameter +1 embeds canonically into the centers of the stated skein algebras whose deforming parameter is an odd root unity. We also construct an isomorphism between the stated skein algebra at +1 and the algebra of regular function of a generalization of the SL2-character variety of the surface. As a result, we associate to each isomorphism class of irreducible or local representations of the stated skein algebra, an invariant which is a point in the character variety.

References in corpus (2)

• Local representations of the quantum Teichmuller space
• Poisson algebras of curves on bordered surfaces and skein quantization

Cited by in corpus (5)

• Finite presentations for stated skein algebras and lattice gauge field theory
• Triangular decomposition of $S{L}_3$ skein algebras
• Tropical Fock-Goncharov coordinates for ${\mathrm{SL}}_3$-webs on surfaces I: construction
• Quantum holonomic link invariants derived from stated skein algebras
• Stated skein algebras and their representations