Search results for "knots and links"

showing 2 items of 2 documents

The HOMFLY-PT polynomials of sublinks and the Yokonuma–Hecke algebras

2016

We describe completely the link invariants constructed using Markov traces on the Yokonuma-Hecke algebras in terms of the linking matrix and the HOMFLYPT polynomials of sublinks.

MSC: Primary 57M27: Invariants of knots and 3-manifolds Secondary 20C08: Hecke algebras and their representations 20F36: Braid groups; Artin groups 57M25: Knots and links in $S^3$Pure mathematicsMarkov chainGeneral Mathematics010102 general mathematicsYokonuma-Hecke algebrasGeometric Topology (math.GT)Linking numbers01 natural sciencesMathematics::Geometric TopologyMatrix (mathematics)Mathematics - Geometric TopologyMarkov tracesMathematics::Quantum Algebra[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)010307 mathematical physics0101 mathematicsRepresentation Theory (math.RT)Link (knot theory)Mathematics - Representation TheoryMathematics
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A cubic defining algebra for the Links-Gould polynomial

2012

We define a finite-dimensional cubic quotient of the group algebra of the braid group, endowed with a (essentially unique) Markov trace which affords the Links-Grould invariant of knots and links. We investigate several of its properties, and state several conjectures about its structure.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT][MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA][ MATH.MATH-QA ] Mathematics [math]/Quantum Algebra [math.QA]Links-Gould polynomialGeometric Topology (math.GT)braid groupMathematics::Geometric TopologyMarkov traceMathematics - Geometric Topology57M27[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]Mathematics - Quantum AlgebraFOS: Mathematics[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]quantum invariantsQuantum Algebra (math.QA)knots and links[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
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