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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2019, Volume 4, Issue 3, Pages 255–264
DOI: https://doi.org/10.24411/2500-0101-2019-14301 (Mi chfmj143) 		 
Mathematics

On a Yang — Baxter operator and the corresponding knots invariant

K. S. Asaulkoa, F. G. Korablevab

a Chelyabinsk State University, Chelyabinsk, Russia
b N.N.\,Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia
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DOI: https://doi.org/10.24411/2500-0101-2019-14301
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00690_а
The work is supported by the grant of RFBR (project 17-01-00690) and by the Foundation of Promising Research of Chelyabinsk State University.
Received: 19.08.2019
Revised: 14.09.2019
Document Type: Article
UDC: 515.162.8
Language: Russian
Citation: K. S. Asaulko, F. G. Korablev, “On a Yang — Baxter operator and the corresponding knots invariant”, Chelyab. Fiz.-Mat. Zh., 4:3 (2019), 255–264
Citation in format AMSBIB
\Bibitem{AsaKor19}
\by K.~S.~Asaulko, F.~G.~Korablev
\paper On a Yang~--- Baxter operator and the corresponding knots invariant
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2019
\vol 4
\issue 3
\pages 255--264
\mathnet{http://mi.mathnet.ru/chfmj143}
\crossref{https://doi.org/10.24411/2500-0101-2019-14301}
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