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--Hecke algebras, as well as recent results on the framization of the Temperley--Lieb algebra. Finally, we propose framizations for other knot a…
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8 results for “Framization”
Study framizations of algebras using Schur--Weyl duality and tied braids.
problem Understanding framizations of algebras and their connections to quantum groups.
method Developing a general setting for framizations of algebras, including Yokonuma--Hecke and tied braids.
result Obtained Schur--Weyl duality for various algebras, including new framizations.
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 construct a Markov trace on these algebras and from this trace we derive isotopy invariants for framed and classical knots and links in the so…
Extends Framization to Coxeter system of type B.
problem Extending Framization to Coxeter systems of type B.
method Define a natural extension of the classical Temperley-Lieb algebra, prove the existence of a unique linear Markov trace function, introduce Framization as a quotient of the Yokonuma-Hecke algebra, and provide conditions for the Markov trace to pass to the quotient.
result Construct invariants for framed and classical links inside the solid torus.
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 is both algebraically consistent and topologically meaningful. Our framization of the Temperley-Lieb algebra is defined as a quotient of the…
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 algebra, and start a systematic study of this framization. We show that is finite dimensional and the \lq braid generators\rq\ of t…
In this survey we collect all results regarding the construction of the Framization of the Temperley-Lieb algebra of type as a quotient algebra of the Yokonuma-Hecke algebra of type . More precisely, we present all three possible quotient algebras the emerged during this construction and we discuss their dimensi…
In this paper we first present the construction of the new 2-variable classical link invariants arising from the Yokonuma-Hecke algebras , which are not topologically equivalent to the Homflypt polynomial. We then present the algebra which is the appropriate Temperley-Lieb analogu…