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Presentations of Kauffman bracket skein algebras of planar surfaces
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abstract
Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface $\Sigma_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by explicit generators and relations. The presentation is independent of $R$, and can be considered as a quantization of the trace algebra of $n$ generic $2\times 2$ unimodular matrices.
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Kauffman bracket skein algebra of the 4-holed disk
The paper gives a monomial basis and a finite presentation for the Kauffman bracket skein algebra of the 4-holed disk over Z[q^{±1/2}], extending previous coefficient fields and adding a character variety freeness theorem.
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