Convergent star products on cotangent bundles of Lie groups
Please always quote using this URN: urn:nbn:de:bvb:20-opus-324324
- For a connected real Lie group G we consider the canonical standard-ordered star product arising from the canonical global symbol calculus based on the half-commutator connection of G. This star product trivially converges on polynomial functions on T\(^*\)G thanks to its homogeneity. We define a nuclear Fréchet algebra of certain analytic functions on T\(^*\)G, for which the standard-ordered star product is shown to be a well-defined continuous multiplication, depending holomorphically on the deformation parameter \(\hbar\). This nuclearFor a connected real Lie group G we consider the canonical standard-ordered star product arising from the canonical global symbol calculus based on the half-commutator connection of G. This star product trivially converges on polynomial functions on T\(^*\)G thanks to its homogeneity. We define a nuclear Fréchet algebra of certain analytic functions on T\(^*\)G, for which the standard-ordered star product is shown to be a well-defined continuous multiplication, depending holomorphically on the deformation parameter \(\hbar\). This nuclear Fréchet algebra is realized as the completed (projective) tensor product of a nuclear Fréchet algebra of entire functions on G with an appropriate nuclear Fréchet algebra of functions on \({\mathfrak {g}}^*\). The passage to the Weyl-ordered star product, i.e. the Gutt star product on T\(^*\)G, is shown to preserve this function space, yielding the continuity of the Gutt star product with holomorphic dependence on \(\hbar\).…
Author: | Michael Heins, Oliver Roth, Stefan WaldmannORCiD |
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URN: | urn:nbn:de:bvb:20-opus-324324 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Parent Title (English): | Mathematische Annalen |
ISSN: | 0025-5831 |
Year of Completion: | 2023 |
Volume: | 386 |
Issue: | 1-2 |
Pagenumber: | 151-206 |
Source: | Mathematische Annalen (2023) 386:1-2, 151-206 DOI: 10.1007/s00208-022-02384-x |
DOI: | https://doi.org/10.1007/s00208-022-02384-x |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | Lie groups; star products |
Release Date: | 2024/03/11 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |