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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

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

Bibliographic databases:

UDC: 517.986
Received: March 15, 2018

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
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\pages 316--333
\publ MAIK Nauka/Interperiodica
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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