Skein algebras of surfaces

Przytycki, Józef; Sikora, Adam

doi:10.1090/tran/7298

Skein algebras of surfaces
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by Józef H. Przytycki and Adam S. Sikora PDF

Trans. Amer. Math. Soc. 371 (2019), 1309-1332 Request permission

Abstract:

We show that the Kauffman bracket skein algebra of any oriented surface $F$ (possibly with marked points in its boundary) has no zero divisors and that its center is generated by knots parallel to the unmarked components of the boundary of $F$. Furthermore, we show that skein algebras are Noetherian and Ore. Our proofs rely on certain filtrations of skein algebras induced by pants decompositions of surfaces. We prove some basic algebraic properties of the associated graded algebras along the way.

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