The A-polynomial from the noncommutative viewpoint
type: Item
instance of: scholarly article
title: The A-polynomial from the noncommutative viewpoint
zbMATH Open document ID: 0980.57002
DOI: 10.1090/S0002-9947-01-02889-6
author: Răzvan Gelca
author: Walter LoFaro
author: Charles Frohman
published in: Transactions of the American Mathematical Society
publication date: 2001-12-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/9812048
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 46L87
zbMATH DE Number: 1680732
zbMATH Keywords: Kauffman bracket
zbMATH Keywords: skein modules
zbMATH Keywords: A-polynomial
zbMATH Keywords: character varieties
zbMATH Keywords: noncommutative geometry
MaRDI profile type: Publication
arXiv ID: math/9812048
cites work: Q4305609
cites work: A finite set of generators for the Kauffman bracket skein algebra
cites work: 𝑆𝐿(2) Representations of Finitely Presented Groups
cites work: Q5639812
cites work: Plane curves associated to character varieties of 3-manifolds
cites work: Representation theory and the \(A\)-polynomial of a knot
cites work: Q4310044
cites work: Varieties of group representations and splittings of 3-manifolds
cites work: Skein modules and the noncommutative torus
cites work: Non-commutative trigonometry and the A-polynomial of the trefoil knot
cites work: THE (2, ∞)-SKEIN MODULE OF WHITEHEAD MANIFOLDS
cites work: Q4317887
cites work: On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties
cites work: Q4367595
cites work: On skein algebras and \(Sl_2(\mathbb{C})\)-character varieties
cites work: C*-algebras associated with irrational rotations
cites work: Deformation quantization of Heisenberg manifolds
cites work: Skeins and mapping class groups
cites work: Q4351008
cites work: Contact surgery and symplectic handlebodies
OpenAlex ID: W1574065017
review text: 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.
reviewed by: Leila Ben Abdelghani
description: scientific article; zbMATH DE number 1680732