Graded Lie Algebras and Dynamical Systems

Author: Vershik A.M.

Source: Acta Applicandae Mathematicae, Volume 73, Numbers 1-2, August 2002 , pp. 239-249(11)

Publisher: Springer

Abstract:

We define the graded Lie algebras generated by ergodic transformation with invariant measure. This algebra is the central extension of Lie algebras which is associated with the usual crossed product. At the same time, it is the special case of algebras with continuum root systems which were defined by the author and M. Saveliev at the beginning of Nineties. Examples of systems with a discrete spectrum are considered.

Keywords: graded Lie algebras; root systems; ergodic transformation; central extension

Language: English

Document Type: Research article

Affiliations: 1: St. Petersburg Division, Steklov Mathematical Institute, RAS, 27, Fontanka, St. Petersburg, 191011, Russia. e-mail: vershik@pdmi.ras.ru

Publication date: 2002-08-01

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