Lie Algebras of Differential Operators in Two Complex Variables
نویسندگان
چکیده
منابع مشابه
Lie Algebras of Differential Operators and Lie-Algebraic Potentials
An explicit characterisation of all second order differential operators on the line which can be written as bilinear combinations of the generators of a linitedimensional Lie algebra of first order differential operators is found, solving a problem arising in the Lie-algebraic approach to scattering theory and molecular dynamics. One-dimensional potentials corresponding to these Lie algebras ar...
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(i) Tr(DiA) = 0 for any A ∈ A and any Di ∈ D (ii) [Di,Dj ] = ad(Qij) — inner derivation (Qij ∈ A) for any Di,Dj ∈ D (iii) Alt i,j,k Dk(Qij) = 0 for all i, j, k. The main example of such a situation is the Lie algebra ΨDifn(S 1) of the formal pseudodifferential operators on (S1)n (see [A]). The trace Tr in this example is the “noncommutative residue”, Tr(D) = the coefficient of the term x 1 · x ...
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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...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 1992
ISSN: 0002-9327
DOI: 10.2307/2374757