  We generalize the positivity conjecture of (Kauffman bracket) skein algebras
to Roger--Yang skein algebras. To generalize it, we use explicit polynomials
like Chebyshev polynomials of the first kind to give candidates of positive
bases. Moreover, the polynomials form a lower bound in the sense of [L\^e18]
and [LTY21]. We also discuss a relation between the polynomials and the centers
of Roger--Yang skein algebras when the quantum parameter is a complex root of
unity.

Geometric Topology;Quantum Algebra;Rings and Algebras