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Petersburg Department of Steklov Institute of Mathematics

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PREPRINT 21/1999

б.н.четыйл, в.в.ыпкиеф
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зтбдхйтпчбооще бмзевтщ мй, лбтфбопчулбс рпдбмзевтб
лпфптщи еуфш бмзевтб нопзпюмеопч пдопк ретенеоопк

This preprint was accepted оПСВТШ, 1999

Contact:
` б.н.чЕТЫЙЛ `

ABSTRACT:
We define a class of infinite dimensional Lie algebras
which generalize universal covering of $sl(2,C)$ as Lie algebras
([5,9,8,6]). These algebras are the partial case of $Z$-graded
Lie algebras with continious root systems ([1,2,10]), namely,
the Cartan subalgebra of its is algebra of polynomials of one
variable. Continious limit of such algebras gives a new Poisson
brackets on the algebraic surfaces.

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