2-cocycles on the Lie Algebras of Generalized Differential Operators
نویسنده
چکیده
In a recent paper by Zhao and the author, the Lie algebras A[D] = A⊗ IF [D] of Weyl type were defined and studied, where A is a commutative associative algebra with an identity element over a field IF of any characteristic, and IF [D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, the 2-cocycles of a class of the above Lie algebras A[D] (which are called the Lie algebras of generalized differential operators in the present paper), with IF 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. §
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تاریخ انتشار 2000