OPERATOR PENCIL PASSING THROUGH A GIVEN OPERATOR
OPERATOR PENCIL PASSING THROUGH A GIVEN OPERATOR
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操作员铅笔穿过指定操作员
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
H. Khudaverdian
中科院分区：
文献类型：
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作者：
A. Biggs;H. Khudaverdian
令 Δ 为作用于流形 M 上给定权重 λ0 的密度空间的线性微分算子。可以考虑一束算子 Π(Δ)={Δλ} 穿过算子 Δ，使得任何 Δλ 都是作用于权重 λ 的密度的线性微分算子。这支铅笔可以用作用于所有权重的密度代数的线性微分算子 Δ 来识别。密度代数中不变标量积的存在意味着算子的自然分解，即自伴算子和反自伴算子的铅笔。我们研究的提升映射一方面与无散向量场等变，另一方面具有自伴随或反自伴随算子中的值。特别是，我们分析了这两个概念之间的关系，并将其应用于 diff (M) 等变提升的研究。最后，我们简要考虑关于射影变换代数的提升等变的情况并描述...
Let Δ be a linear differential operator acting on the space of densities of a given weight λ0 on a manifold M. One can consider a pencil of operators Π(Δ)={Δλ} passing through the operator Δ such that any Δλ is a linear differential operator acting on densities of weight λ. This pencil can be identified with a linear differential operator Δ acting on the algebra of densities of all weights. The existence of an invariant scalar product in the algebra of densities implies a natural decomposition of operators, i.e., pencils of self-adjoint and anti-self-adjoint operators. We study lifting maps that are on one hand equivariant with respect to divergenceless vector fields, and, on the other hand, with values in self-adjoint or anti-self-adjoint operators. In particular, we analyze the relation between these two concepts, and apply it to the study of diff (M)-equivariant liftings. Finally, we briefly consider the case of liftings equivariant with respect to the algebra of projective transformations and descri...