Space of second order linear differential operators as a module over the Lie algebra of vector fields
Space of second order linear differential operators as a module over the Lie algebra of vector fields
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作为矢量场李代数上的模的二阶线性微分算子空间
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
V. Ovsienko
中科院分区：
文献类型：
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作者：
C. Duval;V. Ovsienko
光滑流形M上的线性微分算子空间具有自然的单参数Diff（M）-（和Vect（M）-）模结构族，由它们在张量密度空间上的作用定义。证明了在二阶微分算子的情形下，除了三个临界值{0，12，1}外，对于任何张量密度阶数，向量（M）模结构都是等价的.李导数的二阶类似物出现在张量密度上的二阶微分算子空间之间的交织算子。
Abstract The space of linear differential operators on a smooth manifoldMhas a natural one-parameter family of Diff(M)- (and Vect(M)-) module structures, defined by their action on the space of tensor densities. It is shown that, in the case of second-order differential operators, the Vect(M)-module structures are equivalent, for any degree of tensor densities except for three critical values; {0, 1 2 , 1}. A second-order analogue of the Lie derivative appears as an intertwining operator between the spaces of second-order differential operators on tensor densities.