Matematicheskii Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2006, Volume 197, Number 1, Pages 39–54 (Mi msb1495)  

This article is cited in 5 scientific papers (total in 5 papers)

Geometry of operator cross ratio

M. I. Zelikin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The operator cross ratio, which is meaningful, in particular, for the infinite-dimensional Sato Grassmannian is defined and investigated. Its homological interpretation is presented. A matrix and operator analogue of the Schwartzian differential operator is introduced and its relation to linear Hamiltonian systems and Riccati's equation is established. The aim of these constructions is application to the KP-hierarchy (the Kadomtsev–Petviashvili hierarchy).
Bibliography: 12 titles.

DOI: https://doi.org/10.4213/sm1495

Full text: PDF file (484 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2006, 197:1, 37–51

Bibliographic databases:

UDC: 512.542+517.551
MSC: 37K10, 37K20
Received: 21.03.2005

Citation: M. I. Zelikin, “Geometry of operator cross ratio”, Mat. Sb., 197:1 (2006), 39–54; Sb. Math., 197:1 (2006), 37–51

Citation in format AMSBIB
\Bibitem{Zel06}
\by M.~I.~Zelikin
\paper Geometry of operator cross ratio
\jour Mat. Sb.
\yr 2006
\vol 197
\issue 1
\pages 39--54
\mathnet{http://mi.mathnet.ru/msb1495}
\crossref{https://doi.org/10.4213/sm1495}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2230131}
\zmath{https://zbmath.org/?q=an:1144.37031}
\elib{https://elibrary.ru/item.asp?id=9188970}
\transl
\jour Sb. Math.
\yr 2006
\vol 197
\issue 1
\pages 37--51
\crossref{https://doi.org/10.1070/SM2006v197n01ABEH003745}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000237780600003}
\elib{https://elibrary.ru/item.asp?id=14317935}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33744746951}


Linking options:
  • http://mi.mathnet.ru/eng/msb1495
  • https://doi.org/10.4213/sm1495
  • http://mi.mathnet.ru/eng/msb/v197/i1/p39

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Dimakis A., Müller-Hoissen F., “Weakly nonassociative algebras, Riccati and KP hierarchies”, Generalized Lie theory in mathematics, physics and beyond, Springer, Berlin, 2009, 9–27  crossref  mathscinet  zmath  isi  scopus
    2. Dupré M.J., Glazebrook J.F., Previato E., “Curvature of universal bundles of Banach algebras \invook Topics in operator theory. Volume 1. Operators, matrices and analytic functions”, Oper. Theory Adv. Appl., 202, Birkhäuser Verlag, Basel, 2010, 195–222  mathscinet  zmath  isi
    3. Previato E., “Sigma function and dispersionless hierarchies”, XXIX Workshop on Geometric Methods in Physics, AIP Conf. Proc., 1307, Amer. Inst. Phys., Melville, NY, 2010, 140–156  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Dupre M.J., Glazebrook J.F., Previato E., “Differential Algebras with Banach-Algebra Coefficients I: From $C^*$-Algebras to the K-Theory of the Spectral Curve”, Complex Anal. Oper. Theory, 7:4 (2013), 739–763  crossref  mathscinet  zmath  isi  scopus
    5. Dupre M.J., Glazebrook J.F., Previato E., “Differential Algebras with Banach-Algebra Coefficients II: the Operator Cross-Ratio Tau-Function and the Schwarzian Derivative”, Complex Anal. Oper. Theory, 7:6 (2013), 1713–1734  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:473
    Full text:253
    References:37
    First page:3

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022