Skein algebras of surfaces

We show that the Kauffman bracket skein algebra of any oriented surface FF (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 FF. Furthermore, we show that skein algebras are Noetherian a...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2019-01, Vol.371 (2), p.1309-1332
Main Authors: Przytycki, Józef H., Sikora, Adam S.
Format: Article
Language:English
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Research article
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Summary:We show that the Kauffman bracket skein algebra of any oriented surface FF (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 FF. 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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7298