Three-partite vertex model and knot invariants
Kassenova T.K. Tsyba P.Y. Razina O.V. Myrzakulov R.
1 July 2022Elsevier B.V.
Physica A: Statistical Mechanics and its Applications
2022#597
This work is dedicated to the consideration of the construction of a representation of braid group generators from vertex models with N-states, which provides a great way to study the knot invariant. An algebraic formula is proposed for the knot invariant when different spins (N−1)/2 are located on all components of the knot. The work summarizes procedure outputting braid generator representations from three-partite vertex model. This representation made it possible to study the invariant of a knot with multi-colored links, where the components of the knot have different spins. The formula for the invariant of knot with a multi-colored link is studied from the point of view of the braid generators obtained from the R-matrices of three-partite vertex models. The resulting knot invariant 52 corresponds to the Jones polynomial and HOMFLY-PT.
Braid group , Knots theory , Vertex model
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L.N. Gumilyov Eurasian National University, Eurasian International Centre Theoretical Physics, Nur-Sultan, Kazakhstan
M.Kh.Dulaty Taraz Regional University, Taraz, Kazakhstan
LLP Ratbay Myrzakulov Eurasian International Center for Theoretical Physics, Nur-Sultan, Kazakhstan
L.N. Gumilyov Eurasian National University
M.Kh.Dulaty Taraz Regional University
LLP Ratbay Myrzakulov Eurasian International Center for Theoretical Physics
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