- Author
- Marianna Chatzakou (UGent)
- Organization
- Abstract
- This work aims to develop a global quantization in the concrete settings of two graded nilpotent Lie groups of 3-step; namely of the Engel group and the Cartan group. We provide a preliminary analysis on the structure and the representations of the aforementioned groups, and their corresponding Lie algebras. In addition, the explicit formulas for the difference operators in the two settings are derived, constituting the necessary prerequisites for the constructions of the.m.,d classes of symbols in both cases. In the case of the Engel group, the relation between the Kohn-Nirenberg quantization and the representations of the Engel group enables us to express operators in this setting in terms of quantization of symbols in the Euclidean space.
- Keywords
- Engel group, Cartan group, difference operators, quantization formula, OPERATORS
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8713860
- MLA
- Chatzakou, Marianna. “Quantizations on the Engel and the Cartan Groups.” JOURNAL OF LIE THEORY, vol. 31, no. 2, 2021, pp. 517–42.
- APA
- Chatzakou, M. (2021). Quantizations on the Engel and the Cartan groups. JOURNAL OF LIE THEORY, 31(2), 517–542.
- Chicago author-date
- Chatzakou, Marianna. 2021. “Quantizations on the Engel and the Cartan Groups.” JOURNAL OF LIE THEORY 31 (2): 517–42.
- Chicago author-date (all authors)
- Chatzakou, Marianna. 2021. “Quantizations on the Engel and the Cartan Groups.” JOURNAL OF LIE THEORY 31 (2): 517–542.
- Vancouver
- 1.Chatzakou M. Quantizations on the Engel and the Cartan groups. JOURNAL OF LIE THEORY. 2021;31(2):517–42.
- IEEE
- [1]M. Chatzakou, “Quantizations on the Engel and the Cartan groups,” JOURNAL OF LIE THEORY, vol. 31, no. 2, pp. 517–542, 2021.
@article{8713860,
abstract = {{This work aims to develop a global quantization in the concrete settings of two graded nilpotent Lie groups of 3-step; namely of the Engel group and the Cartan group. We provide a preliminary analysis on the structure and the representations of the aforementioned groups, and their corresponding Lie algebras. In addition, the explicit formulas for the difference operators in the two settings are derived, constituting the necessary prerequisites for the constructions of the.m.,d classes of symbols in both cases. In the case of the Engel group, the relation between the Kohn-Nirenberg quantization and the representations of the Engel group enables us to express operators in this setting in terms of quantization of symbols in the Euclidean space.}},
author = {{Chatzakou, Marianna}},
issn = {{0949-5932}},
journal = {{JOURNAL OF LIE THEORY}},
keywords = {{Engel group,Cartan group,difference operators,quantization formula,OPERATORS}},
language = {{eng}},
number = {{2}},
pages = {{517--542}},
title = {{Quantizations on the Engel and the Cartan groups}},
volume = {{31}},
year = {{2021}},
}