Abstract
We are interested in the classification of left-invariant symplectic structures on Lie groups. Some classifications are known, especially in low dimensions. In this paper we establish a new approach to classify (up to automorphism and scale) left-invariant symplectic structures on Lie groups. The procedure is based on the moduli space of left-invariant nondegenerate 2-forms. Then we apply our procedure for two particular Lie groups of dimension 2n and give classifications of left-invariant symplectic structures on them.
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This article was funded by Japan Society for the Promotion of Science (Grant no. 19K21831).
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This work was partly supported by Osaka City University Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849). The second author was supported by JSPS KAKENHI Grant Number 19K21831.
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Castellanos Moscoso, L.P., Tamaru, H. A classification of left-invariant symplectic structures on some Lie groups. Beitr Algebra Geom 64, 471–491 (2023). https://doi.org/10.1007/s13366-022-00643-1
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DOI: https://doi.org/10.1007/s13366-022-00643-1