2000/12/03 by Yucai Su, Su, Yucai
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA
paper · pdf · doi:10.48550/arxiv.math/0012014
15 pages, Latex, to appear in Comm. Alg
arxiv created 2000/12/03 · arxiv updated 2009/11/30
In a recent paper by Zhao and the author, the Lie algebras A[D]=A⊗ F[D] of Weyl type were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[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 F 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.