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Three-partite vertex model and knot invariants

Author

Listed:
  • Kassenova, T.K.
  • Tsyba, P.Yu.
  • Razina, O.V.
  • Myrzakulov, R.

Abstract

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.

Suggested Citation

  • Kassenova, T.K. & Tsyba, P.Yu. & Razina, O.V. & Myrzakulov, R., 2022. "Three-partite vertex model and knot invariants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    • Handle: RePEc:eee:phsmap:v:597:y:2022:i:c:s0378437122002400
    DOI: 10.1016/j.physa.2022.127283
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    References listed on IDEAS

    as
    1. Jin, Xian'an & Zhang, Fuji, 2004. "Jones polynomials and their zeros for a family of links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 183-196.
    2. Chang, S.-C. & Shrock, R., 2001. "Zeros of Jones polynomials for families of knots and links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 196-218.
    3. Jin, Xian'an & Zhang, Fuji, 2003. "Zeros of the Jones polynomials for families of pretzel links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(3), pages 391-408.
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    1. Jin, Xian'an & Zhang, Fuji, 2004. "Jones polynomials and their zeros for a family of links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 183-196.
    2. Jin, Xian'an & Zhang, Fuji, 2003. "Zeros of the Jones polynomials for families of pretzel links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(3), pages 391-408.

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