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Petersburg Department of Steklov Institute of Mathematics

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PREPRINT 8/1999

B.SHOIKHET AND A.VERSHIK
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LIE ALGEBRAS WITH CONTINUAL ROOTS
SYSTEM CARTAN SUBALGEBRA OF
WHICH IS C[h]

This preprint was accepted April 12, 1999

Contact:
` A.M.Vershik `

ABSTRACT:
We describe Lie algebras with continual root system in
sense Vershik--Saveliev Cartan subalgebra of which is algebra of
polynomials of one variable.
We can define the algebras of this type in canonical form with
Cartan operator or in the form of cross-product corresponding to
some dynamical system with 2-cocycle and their limit. In the
last case we have Lie algebra of Poisson brackets on the
surface.

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