Operator pencils on the algebra of densities

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• 作者：A. Biggs (1)
  H. M. Khudaverdian (1)
  
• 刊名：Proceedings of the Steklov Institute of Mathematics
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：286
• 期：1
• 页码：33-54
• 全文大小：1,359 KB
• 参考文献：1. A. Biggs, 鈥淕eometric structures on the algebra of densities,鈥?PhD Thesis (Univ. Manchester, 2014).
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  7. H. M. Khudaverdian and Th. Th. Voronov, 鈥淪econd order operators on the algebra of densities and a groupoid of connections,鈥?Preprint No. 73 (Max-Planck-Inst. Math., Bonn, 2011).
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• 作者单位：A. Biggs (1)
  H. M. Khudaverdian (1)
  
  1. School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
  
• ISSN：1531-8605

文摘

We continue to study equivariant pencil liftings and differential operators on the algebra of densities. We emphasize the role played by the geometry of the extended manifold where the algebra of densities is a special class of functions. Firstly we consider basic examples. We give a projective line of diff(M)-equivariant pencil liftings for first order operators and describe the canonical second order self-adjoint lifting. Secondly we study pencil liftings equivariant with respect to volume preserving transformations. This helps to understand the role of self-adjointness for the canonical pencils. Then we introduce the Duval-Lecomte-Ovsienko (DLO) pencil lifting which is derived from the full symbol calculus of projective quantisation. We use the DLO pencil lifting to describe all regular proj-equivariant pencil liftings. In particular, the comparison of these pencils with the canonical pencil for second order operators leads to objects related to the Schwarzian.