\(p\)-adic framed braids. II
type: Item
instance of: scholarly article
title: \(p\)-adic framed braids. II
zbMATH Open document ID: 1266.57011
author: Jesús Juyumaya
author: Sofia Lambropoulou
published in: Advances in Mathematics
publication date: 2013-02-11T00:00:00Z
review text: The authors work to define modular and \(p\)-adic framed link invariants of trace type. As this requires certain conditions to be satisfied by complex trace parameters, solutions to a set of non-linear equations are needed. These are supplied in an Appendix by Paul Gerardin. The bulk of the paper is taken up by the study of both the modular and \(p\)-adic framed braid groups, in particular the algebras arising from them. The (Yokonuma-Hecke) algebras associated with the \(p\)-adic framed braid groups were constructed by the authors in [Topology Appl. 154, No. 8, 1804--1826 (2007; Zbl 1165.57007)] as inverse limits. This paper is a sequel to that one, and refines and expands those results, especially examining certain dense subalgebras and approximations using them. Both a modular and \(p\)-adic trace are constructed and it is from these that the link invariants are eventually derived. A number of examples of the modular framed link invariant are presented.
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 20F38
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 6135750
zbMATH Keywords: framed braid
zbMATH Keywords: framed link
zbMATH Keywords: Yokonuma-Hecke algebra
zbMATH Keywords: \(p\)-adic integers
zbMATH Keywords: modular framed link
zbMATH Keywords: \(p\)-adic framed link
zbMATH Keywords: isotopy invariant
zbMATH Keywords: Markov trace
reviewed by: Lee P. Neuwirth
MaRDI profile type: Publication
full work available at URL: j.aim.2012.10.011
OpenAlex ID: W2013869453
cites work: THE YOKONUMA–HECKE ALGEBRAS AND THE HOMFLYPT POLYNOMIAL
cites work: On the link invariants from the Yokonuma-Hecke algebras
cites work: The Yokonuma–Temperley–Lieb algebra
cites work: Hecke algebra representations of braid groups and link polynomials
cites work: MARKOV TRACE ON THE YOKONUMA–HECKE ALGEBRA
cites work: \(p\)-adic framed braids
cites work: An Adelic Extension of the Jones Polynomial
cites work: AN INVARIANT FOR SINGULAR KNOTS
cites work: On the Framization of Knot Algebras
cites work: The Framed Braid Group and 3-Manifolds
cites work: Q4490702
cites work: Q4217279
cites work: Q5631299
DOI: 10.1016/J.AIM.2012.10.011
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description: scientific article; zbMATH DE number 6135750