Tr. Mat. Inst. Steklova, 2018, Volume 302, Pages 316–333
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
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).
|Russian Science Foundation
|This work is supported by the Russian Science Foundation under grant 14-11-00414.
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Proceedings of the Steklov Institute of Mathematics, 2018, 302, 298–314
Received: March 15, 2018
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
\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
\publ MAIK Nauka/Interperiodica
\jour Proc. Steklov Inst. Math.
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