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arXiv · 2012.01710

A classification of left-invariant symplectic structures on some Lie groups

Luis Pedro Castellanos Moscoso·Hiroshi Tamaru
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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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Luis Pedro Castellanos Moscoso, Hiroshi Tamaru. 2020-12-03. A classification of left-invariant symplectic structures on some Lie groups. https://doi.org/10.1007/s13366-022-00643-1

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