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

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 pr...

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Bibliographic Details
Published inBeiträge zur Algebra und Geometrie Vol. 64; no. 2; pp. 471 - 491
Main Authors Castellanos Moscoso, Luis Pedro, Tamaru, Hiroshi
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2023
Springer Nature B.V
Subjects
Algebra
Algebraic Geometry
Automorphisms
Classification
Convex and Discrete Geometry
Geometry
Invariants
Lie groups
Mathematics
Mathematics and Statistics
Original Paper
Primary 53C30
Secondary 53D05
22E25
Symplectic QR decomposition
Symplectic Lie group
Left-invariant symplectic structures
Moduli space
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Summary: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 2 n and give classifications of left-invariant symplectic structures on them.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-022-00643-1