The classical limit for stated SL n -skein modules

Let [Formula: see text] be a marked 3-manifold. We use [Formula: see text] to denote the stated [Formula: see text]-skein module of [Formula: see text] where [Formula: see text] is a nonzero complex number. We establish a surjective algebra homomorphism from [Formula: see text] to the coordinate ring of some algebraic set, and prove its kernel consists of all nilpotents. We prove the universal representation algebra of [Formula: see text] is isomorphic to [Formula: see text] when [Formula: see text] is connected and [Formula: see text] has only one component. Furthermore, we show [Formula: see text] is isomorphic to [Formula: see text] as algebras, where [Formula: see text] is a connected marked 3-manifold with [Formula: see text], and [Formula: see text] is obtained from [Formula: see text] by adding one extra marking.