RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 Tr. Mat. Inst. Steklova, 2008, Volume 263, Pages 216–226 (Mi tm793)

Lax Operator Algebras and Integrable Hierarchies

O. K. Sheinmanab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Independent University of Moscow

Abstract: We study applications of a new class of infinite-dimensional Lie algebras, called Lax operator algebras, which goes back to the works by I. Krichever and S. Novikov on finite-zone integration related to holomorphic vector bundles and on Lie algebras on Riemann surfaces. Lax operator algebras are almost graded Lie algebras of current type. They were introduced by I. Krichever and the author as a development of the theory of Lax operators on Riemann surfaces due to I. Krichever, and further investigated in a joint paper by M. Schlichenmaier and the author. In this article we construct integrable hierarchies of Lax equations of that type.

Full text: PDF file (200 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 263, 204–213

Bibliographic databases:

Document Type: Article
UDC: 512.554.32

Citation: O. K. Sheinman, “Lax Operator Algebras and Integrable Hierarchies”, Geometry, topology, and mathematical physics. I, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 263, MAIK Nauka/Interperiodica, Moscow, 2008, 216–226; Proc. Steklov Inst. Math., 263 (2008), 204–213

Citation in format AMSBIB
\Bibitem{She08} \by O.~K.~Sheinman \paper Lax Operator Algebras and Integrable Hierarchies \inbook Geometry, topology, and mathematical physics.~I \bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday \serial Tr. Mat. Inst. Steklova \yr 2008 \vol 263 \pages 216--226 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm793} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2599381} \zmath{https://zbmath.org/?q=an:1235.37022} \elib{http://elibrary.ru/item.asp?id=11640644} \transl \jour Proc. Steklov Inst. Math. \yr 2008 \vol 263 \pages 204--213 \crossref{https://doi.org/10.1134/S0081543808040159} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000263177700014} \elib{http://elibrary.ru/item.asp?id=13592056} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-59849103863} 

• http://mi.mathnet.ru/eng/tm793
• http://mi.mathnet.ru/eng/tm/v263/p216

 SHARE:

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

This publication is cited in the following articles:
1. O. K. Sheinman, “Lax operator algebras and Hamiltonian integrable hierarchies”, Russian Math. Surveys, 66:1 (2011), 145–171
•  Number of views: This page: 152 Full text: 16 References: 25 First page: 12