A. V. Smirnov, “Integrable $sl(N,\mathbb C)$ tops as Calogero–Moser systems”, TMF, 158:3 (2009), 355–369; Theoret. and Math. Phys., 158:3 (2009), 300

Loading [MathJax]/jax/output/SVG/config.js

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 158, Number 3, Pages 355–369
DOI: https://doi.org/10.4213/tmf6319 (Mi tmf6319)

This article is cited in 9 scientific papers (total in 9 papers)

Integrable $sl(N,\mathbb C)$ tops as Calogero–Moser systems

A. V. Smirnov

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Full-text PDF (402 kB) Citations (9)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf6319

Abstract: We show a relation between systems of integrable tops on the algebras $sl(N,\mathbb C)$ and Calogero–Moser systems of $N$ particles. We construct classical Lax operators corresponding to these systems. We show that these operators are related to certain new trigonometric and rational solutions of the Yang–Baxter equations for the algebras $sl(N,\mathbb C)$ and give explicit formulas for $N=2,3$.

Keywords: integrable system, Euler–Arnold top, Yang–Baxter equation.

Received: 06.06.2008

English version:
Theoretical and Mathematical Physics, 2009, Volume 158, Issue 3, Pages 300–312
DOI: https://doi.org/10.1007/s11232-009-0024-4

Bibliographic databases:

Language: Russian

Citation: A. V. Smirnov, “Integrable $sl(N,\mathbb C)$ tops as Calogero–Moser systems”, TMF, 158:3 (2009), 355–369; Theoret. and Math. Phys., 158:3 (2009), 300–312

Citation in format AMSBIB

\Bibitem{Smi09}

\by A.~V.~Smirnov

\paper Integrable $sl(N,\mathbb C)$ tops as Calogero--Moser systems

\jour TMF

\yr 2009

\vol 158

\issue 3

\pages 355--369

\mathnet{http://mi.mathnet.ru/tmf6319}

\crossref{https://doi.org/10.4213/tmf6319}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2547446}

\zmath{https://zbmath.org/?q=an:1175.70006}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2009TMP...158..300S}

\transl

\jour Theoret. and Math. Phys.

\yr 2009

\vol 158

\issue 3

\pages 300--312

\crossref{https://doi.org/10.1007/s11232-009-0024-4}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000264844000003}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-63849220192}

Linking options:

https://www.mathnet.ru/eng/tmf6319

https://doi.org/10.4213/tmf6319

https://www.mathnet.ru/eng/tmf/v158/i3/p355

This publication is cited in the following 9 articles:

A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118
Levin A. Olshanetsky M. Zotov A., “Planck Constant as Spectral Parameter in Integrable Systems and Kzb Equations”, J. High Energy Phys., 2014, no. 10, 109
Aminov G. Arthamonov S. Smirnov A. Zotov A., “Rational TOP and Its Classical R-Matrix”, J. Phys. A-Math. Theor., 47:30 (2014), 305207
G. Aminov, S. Arthamonov, “Degenerating the elliptic Schlesinger system”, Theoret. and Math. Phys., 174:1 (2013), 1–20
A. V. Zotov, A. V. Smirnov, “Modifications of bundles, elliptic integrable systems, and related problems”, Theoret. and Math. Phys., 177:1 (2013), 1281–1338
G. Aminov, “Limit relation between Toda chains and the elliptic $SL(N,\mathbb C)$ top”, Theoret. and Math. Phys., 171:2 (2012), 575–588
Andrey M. Levin, Mikhail A. Olshanetsky, Andrey V. Smirnov, Andrei V. Zotov, “Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles”, SIGMA, 8 (2012), 095, 37 pp.
Aminov G., Arthamonov S., “Reduction of the elliptic SL(N, C) top”, Journal of Physics A-Mathematical and Theoretical, 44:7 (2011), 075201
Smirnov A., “Degenerate Sklyanin algebras”, Central European Journal of Physics, 8:4 (2010), 542–554

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	549
Full-text PDF :	283
References:	81
First page:	6

Что такое QR-код?

Registration to the website

Logotypes