The A-polynomial from the noncommutative viewpoint (Q2759074)
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scientific article; zbMATH DE number 1680732
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The A-polynomial from the noncommutative viewpoint |
scientific article; zbMATH DE number 1680732 |
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The A-polynomial from the noncommutative viewpoint (English)
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10 December 2001
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Kauffman bracket
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skein modules
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A-polynomial
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character varieties
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noncommutative geometry
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The authors introduce a noncommutative generalization of the A-polynomial of a knot, called the noncommutative A-ideal. It consists of a finitely generated ideal of polynomials in the quantum plane. For their construction, the authors use the fact that the Kauffman bracket skein algebra of the cylinder over the torus is a subalgebra of the noncommutative torus.NEWLINENEWLINENEWLINESome properties of the noncommutative A-ideal and its relationships with the A-polynomial and the Jones polynomial are discussed.
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