18 citations · 54 across the 16 of their papers we have counts for
24 papers
Party-Hecke algebras
Diego Arcis, Jesús Juyumaya
Party-Hecke algebras are introduced as a two-parameter deformation of party algebras, where one parameter deforms the party generators and the other deforms the elementary transpos…
Framed Blob Monoids
Jesús Juyumaya, Diego Lobos
We introduce and study blob and framed blob monoids. In particular, several realizations of these monoids are given. We compute the cardinality of the framed blob monoid and derive…
Framization and Deframization
Francesca Aicardi, Jesús Juyumaya, Paolo Papi
Starting from the geometric construction of the framed braid group, we define and study the framization of several Brauer-type monoids and also the set partition monoid, all of whi…
Ramified inverse and planar monoids
Francesca Aicardi, Diego Arcis, Jesús Juyumaya
Ramified monoids are a class of monoids introduced by the authors. The main motivation for considering these monoids comes from knot theory, see [3, 4, 5]. Thus, in [2] we have stu…
Brauer and Jones tied monoids
Francesca Aicardi, Diego Arcis, Jesús Juyumaya
We introduce a ramified monoid, attached to each Brauer--type monoid, that is, to the symmetric group, to the Jones and Brauer monoids among others. Ramified monoids correspond to…
An Alexander type invariant for doodles
Bruno Cisneros, Marcelo Flores, Jesús Juyumaya +1
We construct an Alexander type invariant for oriented doodles from a deformation of the Tits representation of the twin group and from the Chebyshev polynomials of second kind. Sim…
Tied Monoids
Diego Arcis, Jesús Juyumaya
We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting…
Polynomial invariants for links and tied links
Jesús Juyumaya
Notes based on lessons given at {\sc Escuela " Fico González Acuña" de Nudos y 3-variedades}, Mérida Yucatán, México, 7--10 (2015) and {\sc Encuentro de nudos, trenzas y álgebras},…
Two parameters bt-algebra and invariants for links and tied links
Francesca Aicardi, Jesus Juyumaya
We introduce a two-parameters bt-algebra which, by specialization, becomes the one-parameter bt-algebra, introduced by the authors, as well as another one-parameter presentation of…
Tied links and invariants for singular links
Francesca Aicardi, Jesus Juyumaya
Tied links and the tied braid monoid were introduced recently by the authors and used to define new invariants for classical links. Here, we give a version purely algebraic-combina…
An algebra involving braids and ties
Francesca Aicardi, Jesus Juyumaya
In this note we study a family of algebras with one parameter defined by generators and relations. The set of generators contains the generators of the usual braids algebra, and an…
Kauffman type invariants for tied links
Francesca Aicardi, Jesus Juyumaya
We define two new invariants for tied links. One of them can be thought as an extension of the Kauffman polynomial and the other one as an extension of the Jones polynomial which i…
A Framization of the Hecke algebra of Type B
Marcelo Flores, Jesus Juyumaya, Sofia Lambropoulou
In this article we introduce a framization of the Hecke algebra of type B. For this framization we construct a faithful tensorial representation and two linear bases. We finally co…
Identifying the invariants for classical knots and links from the Yokonuma-Hecke algebras
Maria Chlouveraki, Jesus Juyumaya, Konstantinos Karvounis +1
In this paper we announce the existence of a family of new -variable polynomial invariants for oriented classical links defined via a Markov trace on the Yokonuma-Hecke algebra…
Tied Links
Francesca Aicardi, Jesus Juyumaya
In this paper we introduce the tied links, i.e. ordinary links provided with some ties between strands. The motivation for introducing such objects originates from a diagrammatical…
Markov trace on the algebra of braids and ties
Francesca Aicardi, Jesus Juyumaya
We prove that the so-called t algebra of braids and ties supports a Markov trace. Further, by using this trace in the Jones' recipe, we define invariant polynomials for classical k…
On the framization of knot algebras
Jesus Juyumaya, Sofia Lambropoulou
This paper presents results on the framization of some knot algebras, defined by the authors. We explain the motivations of the concept of framization, coming from the Yokonuma--He…
A Partition Temperley-Lieb Algebra
Jesús Juyumaya
We introduce a generalization of the Temperley--Lieb algebra. This generalization is defined by adding certain relations to the algebra of braids and ties. A specialization of this…
Framization of the Temperley-Lieb Algebra
Dimos Goundaroulis, Jesus Juyumaya, Aristidis Kontogeorgis +1
We propose a framization of the Temperley-Lieb algebra. The framization is a procedure that can briefly be described as the adding of framing to a known knot algebra in a way that…
The Yokonuma-Temperley-Lieb Algebra
Dimos Goundaroulis, Jesus Juyumaya, Aristides Kontogeorgis +1
In this paper we introduce the Yokonuma-Temperley-Lieb algebra as a quotient of the Yokonuma-Hecke algebra over a two-sided ideal generated by an expression analogous to the one of…
Modular framization of the BMW algebra
Jesus Juyumaya, Sofia Lambropoulou
In this work we introduce the concept of Modular Framization or simply Framization. We construct a framization of the Birman--Wenzl--Murakami algebra, also known as BMW a…
An adelic extension of the Jones polynomial
Jesus Juyumaya, Sofia Lambropoulou
In this paper we represent the classical braids in the Yokonuma--Hecke and the adelic Yokonuma--Hecke algebras. More precisely, we define the completion of the framed braid group a…
An invariant for singular knots
Jesús Juyumaya, Sofia Lambropoulou
In this paper we introduce a Jones-type invariant for singular knots, using a Markov trace on the Yokonuma--Hecke algebras and the theory of singular braids. The…
p-adic framed braids
Jesus Juyumaya, Sofia Lambropoulou
In this paper we define the -adic framed braid group , arising as the inverse limit of the modular framed braids and we give topological generators for…