The Experts below are selected from a list of 52212 Experts worldwide ranked by ideXlab platform
Poulain L Dandecy - One of the best experts on this subject based on the ideXlab platform.
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an isomorphism theorem for yokonuma hecke algebras and applications to link invariants
Mathematische Zeitschrift, 2016Co-Authors: Nicolas Jacon, Poulain L DandecyAbstract:We develop several applications of the fact that the Yokonuma–Hecke algebra of the general linear group GL is isomorphic to a direct Sum of Matrix algebras associated to Iwahori–Hecke algebras of type A . This includes a description of the semisimple and modular representation theory of the Yokonuma–Hecke algebras of GL and a complete classification of all the Markov traces for them. Finally, from these Markov traces, we construct 3-variables polynomials which are invariants for framed and classical knots and links, and investigate their properties with the help of the isomorphism. In particular, for classical knots, a consequence of the construction is that the obtained set of invariants is topologically equivalent to the HOMFLYPT polynomial. We thus recover results of Chlouveraki et al. (2015, arXiv:1505.06666) about the Juyumaya–Lambropoulou invariants.
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an isomorphism theorem for yokonuma hecke algebras and applications to link invariants
arXiv: Representation Theory, 2015Co-Authors: Nicolas Jacon, Poulain L DandecyAbstract:We develop several applications of the fact that the Yokonuma--Hecke algebra of the general linear group GL is isomorphic to a direct Sum of Matrix algebras associated to Iwahori--Hecke algebras of type A. This includes a description of the semisimple and modular representation theory of the Yokonuma--Hecke algebras of GL and a complete classification of all the Markov traces for them. Finally, from these Markov traces, we construct 3-variables polynomials which are invariants for framed and classical knots and links, and investigate their properties with the help of the isomorphism.
Nicolas Jacon - One of the best experts on this subject based on the ideXlab platform.
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an isomorphism theorem for yokonuma hecke algebras and applications to link invariants
Mathematische Zeitschrift, 2016Co-Authors: Nicolas Jacon, Poulain L DandecyAbstract:We develop several applications of the fact that the Yokonuma–Hecke algebra of the general linear group GL is isomorphic to a direct Sum of Matrix algebras associated to Iwahori–Hecke algebras of type A . This includes a description of the semisimple and modular representation theory of the Yokonuma–Hecke algebras of GL and a complete classification of all the Markov traces for them. Finally, from these Markov traces, we construct 3-variables polynomials which are invariants for framed and classical knots and links, and investigate their properties with the help of the isomorphism. In particular, for classical knots, a consequence of the construction is that the obtained set of invariants is topologically equivalent to the HOMFLYPT polynomial. We thus recover results of Chlouveraki et al. (2015, arXiv:1505.06666) about the Juyumaya–Lambropoulou invariants.
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an isomorphism theorem for yokonuma hecke algebras and applications to link invariants
arXiv: Representation Theory, 2015Co-Authors: Nicolas Jacon, Poulain L DandecyAbstract:We develop several applications of the fact that the Yokonuma--Hecke algebra of the general linear group GL is isomorphic to a direct Sum of Matrix algebras associated to Iwahori--Hecke algebras of type A. This includes a description of the semisimple and modular representation theory of the Yokonuma--Hecke algebras of GL and a complete classification of all the Markov traces for them. Finally, from these Markov traces, we construct 3-variables polynomials which are invariants for framed and classical knots and links, and investigate their properties with the help of the isomorphism.
Betul Tanbay - One of the best experts on this subject based on the ideXlab platform.
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The Kadison–Singer problem for the direct Sum of Matrix algebras
Positivity, 2012Co-Authors: Charles Akemann, Joel Anderson, Betul TanbayAbstract:Let M _ n denote the algebra of complex n × n matrices and write M for the direct Sum of the M _ n . So a typical element of M has the form $$ x = x_1\oplus x_2 \cdots \oplus x_n \oplus \cdots, $$ where $${x_n \in M_n}$$ and $${\|x\| = \sup_n\|x_n\|}$$ . We set $${D= \{\{x_n\}\in M: x_n\,{\rm is\,diagonal\,for\,all}\,N\}}$$ . We conjecture (contra Kadison and Singer in Am J Math 81:383–400, 1959 ) that every pure state of D extends uniquely to a pure state of M . This is known for the normal pure states of D, and we show that this is true for a (weak*) open, dense subset of all the singular pure states of D . We also show that (asSuming the Continuum hypothesis) M has pure states that are not multiplicative on any maximal abelian *-subalgebra of M .
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the kadison singer problem for the direct Sum of Matrix algebras
Positivity, 2012Co-Authors: Charles Akemann, Joel Anderson, Betul TanbayAbstract:Let M n denote the algebra of complex n × n matrices and write M for the direct Sum of the M n . So a typical element of M has the form $$ x = x_1\oplus x_2 \cdots \oplus x_n \oplus \cdots, $$ where \({x_n \in M_n}\) and \({\|x\| = \sup_n\|x_n\|}\). We set \({D= \{\{x_n\}\in M: x_n\,{\rm is\,diagonal\,for\,all}\,N\}}\). We conjecture (contra Kadison and Singer in Am J Math 81:383–400, 1959) that every pure state of D extends uniquely to a pure state of M. This is known for the normal pure states of D, and we show that this is true for a (weak*) open, dense subset of all the singular pure states of D. We also show that (asSuming the Continuum hypothesis) M has pure states that are not multiplicative on any maximal abelian *-subalgebra of M.
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The Kadison-Singer problem for the direct Sum of Matrix algebras
arXiv: Operator Algebras, 2010Co-Authors: Charles Akemann, Joel Anderson, Betul TanbayAbstract:Let $M_n$ denote the algebra of complex $n\times n $ matrices and write $M$ for the direct Sum of the $M_n$. So a typical element of $M$ has the form \[x = x_1\oplus x_2 \... \oplus x_n \oplus \...,\] where $x_n \in M_n$ and $\|x\| = \sup_n\|x_n\|$. We set $D= \{\{x_n\} \in M: x_n$ is diagonal for all $N\}$. We conjecture (contra Kadison and Singer (1959)) that every pure state of $D$ extends uniquely to a pure state of $M$. This is known for the normal pure states of D, and we show that this is true for a (weak*) open, dense subset of all the singular pure states of $D$. We also show that (asSuming the Continuum hypothesis) $M$ has pure states that are not multiplicative on any maximal abelian *-subalgebra of $M$.
Maria Chlouveraki - One of the best experts on this subject based on the ideXlab platform.
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From the Framisation of the Temperley–Lieb Algebra to the Jones Polynomial: An Algebraic Approach
Knots Low-Dimensional Topology and Applications, 2019Co-Authors: Maria ChlouverakiAbstract:We prove that the Framisation of the Temperley–Lieb algebra is isomorphic to a direct Sum of Matrix algebras over tensor products of classical Temperley–Lieb algebras. We use this result to obtain a closed combinatorial formula for the invariants for classical links obtained from a Markov trace on the Framisation of the Temperley–Lieb algebra. For a given link L, this formula involves the Jones polynomials of all sublinks of L, as well as linking numbers.
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representation theory and an isomorphism theorem for the framisation of the temperley lieb algebra
Mathematische Zeitschrift, 2017Co-Authors: Maria Chlouveraki, Guillaume PouchinAbstract:In this paper, we describe the irreducible representations and give a dimension formula for the framisation of the Temperley–Lieb algebra. We then prove that the framisation of the Temperley–Lieb algebra is isomorphic to a direct Sum of Matrix algebras over tensor products of classical Temperley–Lieb algebras. This allows us to construct a basis for it. We also study in a similar way the complex reflection Temperley–Lieb algebra.
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Representation theory and an isomorphism theorem for the framisation of the Temperley–Lieb algebra
Mathematische Zeitschrift, 2016Co-Authors: Maria Chlouveraki, Guillaume PouchinAbstract:In this paper, we describe the irreducible representations and give a dimension formula for the framisation of the Temperley–Lieb algebra. We then prove that the framisation of the Temperley–Lieb algebra is isomorphic to a direct Sum of Matrix algebras over tensor products of classical Temperley–Lieb algebras. This allows us to construct a basis for it. We also study in a similar way the complex reflection Temperley–Lieb algebra.
Guillaume Pouchin - One of the best experts on this subject based on the ideXlab platform.
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representation theory and an isomorphism theorem for the framisation of the temperley lieb algebra
Mathematische Zeitschrift, 2017Co-Authors: Maria Chlouveraki, Guillaume PouchinAbstract:In this paper, we describe the irreducible representations and give a dimension formula for the framisation of the Temperley–Lieb algebra. We then prove that the framisation of the Temperley–Lieb algebra is isomorphic to a direct Sum of Matrix algebras over tensor products of classical Temperley–Lieb algebras. This allows us to construct a basis for it. We also study in a similar way the complex reflection Temperley–Lieb algebra.
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Representation theory and an isomorphism theorem for the framisation of the Temperley–Lieb algebra
Mathematische Zeitschrift, 2016Co-Authors: Maria Chlouveraki, Guillaume PouchinAbstract:In this paper, we describe the irreducible representations and give a dimension formula for the framisation of the Temperley–Lieb algebra. We then prove that the framisation of the Temperley–Lieb algebra is isomorphic to a direct Sum of Matrix algebras over tensor products of classical Temperley–Lieb algebras. This allows us to construct a basis for it. We also study in a similar way the complex reflection Temperley–Lieb algebra.
