Geodesic
On a Yang~--- Baxter operator and the corresponding knots invariant
Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 3, pp. 255-264

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The paper is devoted to construction of a Yang — Baxter operator over two-dimensional vector space. Properties of the corresponding invariant of oriented knot and links are studied. An explicit form of the skein relation of this invariant is presented. It's proved, that this invariant is not a consequence of the HOMFLY polynomial. At the end of the paper the table of invariant's values for all oriented knots and links that admit diagrams with at most seven crossing points is given.
Keywords: Yang — Baxter operator, braid group, HOMFLY polynomial, knots invariant. 
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     author = {K. S. Asaulko and F. G. Korablev},
     title = {On a {Yang~---} {Baxter} operator and the corresponding knots invariant},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {255--264},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_3_a0/}
}
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K. S. Asaulko; F. G. Korablev. On a Yang~--- Baxter operator and the corresponding knots invariant. Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 3, pp. 255-264. http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_3_a0/