可解Ricci型辛对称空间的非形式形变量子化
Non-formal deformation quantizations of solvable Ricci-type symplectic symmetric spaces
摘要：
Ricci型辛流形是M. Cahen et al.本文描述了它们在分裂可解对称情形下的形变量子化。特别是，我们介绍了非形式的回火变形量子化的概念，这样的空间。我们证明了回火形变量子化的集合与实直线上的Schwartz算子乘子空间是一一对应的。证明了分裂Ricci型可解对称空间上的不变形式星积是调和非形式量子化的渐近展开。本文通过一个例子说明和部分评论了作者研究的一个关于存在大群对称的非形式量子化的问题。
英文摘要：
Ricci-type symplectic manifolds have been introduced and extensively studied by M. Cahen et al.. In this note, we describe their deformation quantizations in the split solvable symmetric case. In particular, we introduce the notion of non-formal tempered deformation quantization on such a space. We show that the set of tempered deformation quantizations is in one-to-one correspondence with the space of Schwartz operator multipliers on the real line. Moreover we prove that every invariant formal star product on a split Ricci-type solvable symmetric space is an asymptotic expansion of a tempered non-formal quantization. This note illustrates and partially reviews through an example a problematic studied by the author regarding non-formal quantization in presence of large groups of symmetries.
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