Petersburg Department of Steklov Institute of Mathematics

PREPRINT 21/1999

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.