The ideal of relations for two generating sets of skein algebras S_n of the n-holed disk is generated by bounded-degree relations supported on subsurfaces with at most 6 holes (when q+q^{-1} invertible) or n holes (otherwise).
Turaev, Skein quantization of Poisson algebras of loops on surfaces.Ann
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The string cobracket is not a homotopy invariant and the string bracket plus cobracket do not form a Lie bialgebra structure on the S^1-equivariant homology of the free loop space.
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On skein algebras of planar surfaces
The ideal of relations for two generating sets of skein algebras S_n of the n-holed disk is generated by bounded-degree relations supported on subsurfaces with at most 6 holes (when q+q^{-1} invertible) or n holes (otherwise).
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Homotopy Non-Invariance of the String Cobracket and the Failure of the Lie Bialgebra Structure
The string cobracket is not a homotopy invariant and the string bracket plus cobracket do not form a Lie bialgebra structure on the S^1-equivariant homology of the free loop space.