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ABSTRACT
In a recent paper by Zhao and the author, the Lie algebras of Weyl type were defined and studied, where
is a commutative associative algebra with an identity element over a field
of any characteristic, and
is the polynomial algebra of a commutative derivation subalgebra
of
. In the present paper, the 2-cocycles of a class of the above Lie algebras
(which are called the Lie algebras of generalized differential operators in the present paper), with
being a field of characteristic 0, are determined. Among all the 2-cocycles, there is a special one which seems interesting. Using this 2-cocycle, the central extension of the Lie algebra is defined.
ACKNOWLEDGMENT
The author was supported by a fund from Education Department of China.