RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 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, 2018, Volume 302, Pages 316–333 (Mi tm3931)

Polynomial Lie algebras and growth of their finitely generated Lie subalgebras

D. V. Millionshchikov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: The concept of polynomial Lie algebra of finite rank was introduced by V. M. Buchstaber in his studies of new relationships between hyperelliptic functions and the theory of integrable systems. In this paper we prove the following theorem: the Lie subalgebra generated by the frame of a polynomial Lie algebra of finite rank has at most polynomial growth. In addition, important examples of polynomial Lie algebras of countable rank are considered in the paper. Such Lie algebras arise in the study of certain hyperbolic partial differential equations, as well as in the construction of self-similar infinite-dimensional Lie algebras (such as the Fibonacci algebra).

 Funding Agency Grant Number Russian Science Foundation 14-11-00414 This work is supported by the Russian Science Foundation under grant 14-11-00414.

DOI: https://doi.org/10.1134/S0371968518030159

Full text: PDF file (265 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 302, 298–314

Bibliographic databases:

UDC: 517.986

Citation: D. V. Millionshchikov, “Polynomial Lie algebras and growth of their finitely generated Lie subalgebras”, Topology and physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 302, MAIK Nauka/Interperiodica, Moscow, 2018, 316–333; Proc. Steklov Inst. Math., 302 (2018), 298–314

Citation in format AMSBIB
\Bibitem{Mil18} \by D.~V.~Millionshchikov \paper Polynomial Lie algebras and growth of their finitely generated Lie subalgebras \inbook Topology and physics \bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 80th birthday \serial Tr. Mat. Inst. Steklova \yr 2018 \vol 302 \pages 316--333 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3931} \crossref{https://doi.org/10.1134/S0371968518030159} \elib{http://elibrary.ru/item.asp?id=36503447} \transl \jour Proc. Steklov Inst. Math. \yr 2018 \vol 302 \pages 298--314 \crossref{https://doi.org/10.1134/S0081543818060159} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000454896300015} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85059465181}