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pro vyhledávání: '"Sechin, I. A."'
Autor:
Sechin, I. A., Zotov, A. V.
Publikováno v:
Theoret. and Math. Phys., 208:2 (2021) 1156-1164
We construct quadratic quantum algebra based on the dynamical RLL-relation for the quantum $R$-matrix related to $SL(NM)$-bundles with nontrivial characteristic class over elliptic curve. This $R$-matrix generalizes simultaneously the elliptic nondyn
Externí odkaz:
http://arxiv.org/abs/2104.04963
Autor:
Sechin, I., Zotov, A.
Publikováno v:
Theoret. and Math. Phys., 205:1 (2020) 1292-1303
A family of integrable $GL(NM)$ models is described. On the one hand it generalizes the classical spin Ruijsenaars--Schneider systems (the case $N=1$), and on the other hand it generalizes the relativistic integrable tops on $GL(N)$ Lie group (the ca
Externí odkaz:
http://arxiv.org/abs/2011.09599
Autor:
Sechin, I., Zotov, A.
Publikováno v:
Russian Math. Surveys, 74:4 (2019) 767-769
In this letter we construct ${\rm GL}_{NM}$-valued dynamical $R$-matrix by means of unitary skew-symmetric solution of the associative Yang-Baxter equation in the fundamental representation of ${\rm GL}_{N}$. In $N=1$ case the obtained answer reprodu
Externí odkaz:
http://arxiv.org/abs/1905.08724
Publikováno v:
JHEP 10 (2019) 081
We introduce a family of classical integrable systems describing dynamics of $M$ interacting ${\rm gl}_N$ integrable tops. It extends the previously known model of interacting elliptic tops. Our construction is based on the ${\rm GL}_N$ $R$-matrix sa
Externí odkaz:
http://arxiv.org/abs/1905.07820
Autor:
Sechin, I., Zotov, A.
Publikováno v:
Physics Letters B, 781 (2018) 1-7
In this paper we discuss $R$-matrix-valued Lax pairs for ${\rm sl}_N$ Calogero-Moser model and their relation to integrable quantum long-range spin chains of the Haldane-Shastry-Inozemtsev type. First, we construct the $R$-matrix-valued Lax pairs for
Externí odkaz:
http://arxiv.org/abs/1801.08908
Autor:
Sechin, I., Zotov, A.
Publikováno v:
J. Math. Phys. 57 (2016) 053505
In this paper we propose versions of the associative Yang-Baxter equation and higher order $R$-matrix identities which can be applied to quantum dynamical $R$-matrices. As is known quantum non-dynamical $R$-matrices of Baxter-Belavin type satisfy thi
Externí odkaz:
http://arxiv.org/abs/1511.08761
Autor:
Sechin, I. A., Zotov, A. V.
Publikováno v:
Theoretical & Mathematical Physics; Aug2021, Vol. 208 Issue 2, p1156-1164, 9p
Autor:
Sechin, I. A., Zotov, A. V.
Publikováno v:
Theoretical & Mathematical Physics; Oct2020, Vol. 205 Issue 1, p1291-1302, 12p
Autor:
Sechin, I. A., Zotov, A. V.
Publikováno v:
Russian Mathematical Surveys; August 2019, Vol. 74 Issue: 4