Polynomial Lie algebras and growth of their finitely generated Lie subalgebras

D. V. Millionshchikov

Informatics and Automation, Topology and physics, Tome 302 (2018), pp. 316-333.

Résumé

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).

Détail

Keywords: free module, polynomial vector field, Lie–Rinehart algebra, current algebra, loop algebra, growth of a Lie algebra, grading.
Mots-clés : polynomial algebra

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